I'm all for being gracious when receiving a gift and he should accept it from the kids nicely.

But if they're always passive aggressive like that I'd regift or donate it. Does your husband laugh about these or does he want to keep them?

Are they meant to be from the kids to DH, or from her to DH? If it's the latter, he can ask her stop, though there will be drama. 
 

Especially if the gifts are digs at him like the t-shirt was. 

Don't let in ruin your Christmas. Be prepared. Decide on what you will say; can say a thanks, can have a funny comment, be super excited, or just say you will open later. Whatever you do, do not let on it bothers you. Act like you enjoy it. Send "many thanks" home with kids. A little reverse psychology can go a long ways with a toxic BM. LOL

Then once the kids are gone, trash the gifts.

My advice would be to throw it away... Or donate it to a shelter (assuming it's appropriate).  

This is one of those situations that falls in the category of you can't control someone's actions.. but how you react.  If you tell her not to do it?  She wins.. she got to you both.  If you ignore it? You win.. you take back your control from her... and laugh at her patheticness.

"It's so nice that your Mom thought to buy something but since we've already done our shopping together, let's donate this one to (insert charity or church here). "

When my mother sends my children gifts she also includes their half brother because he's little and she doesn't want him to feel left out. They always throw his toy away. I don't send the half anything but it's not nasty intent when my mom sends gifts. I always try to never assume mal-intent.

DBDB only tried this once.  After a few years of living together, I had taken the SS's shopping for DH fathers day gift.  We bought him a jersey of his favorite team and took him to the game.  The night before she had sent with the SS's 3 servings of DH's favorite meal from the restaurant - Seafood pie.  

When we dropped them off after the game, she asked DH all sickly sweet how he liked the pie.  He said oh it was great and I got to eat off of Classy's scallops from hers.  She said, oh but I only sent 3,  I didn't know YOU (me) would have been there.  Well, yes I was there, I live there.  She really looked confused until DH said, you know that youngest SS hates seafood so why would you even send a pie for him?  OMG this woman had NO idea that the son that lived with her does not eat seafood.  Never has and probably never will.  She was so embarrassed.  All gift giving since then has been left upto me.

I would just accept the gift gracefully and then deal with it depending on what it is - give away, throw away, etc.  

never sent gifts; however; once I made Herb-Crusted Rack of Lamb. SS have never had it and tried it.  He loved it!!! A week later he came for his visit with some type of nasty baked lamb in tupperware that BM made. SS then told BF that "Christy is NOT ALLOWED to have any!'  I wouldn't touch that slop anyway!!!

I wouldn't want to touch her slop!!!!!  

Satan was too greedy to dip into "her" money to buy a gift for anyone at all, including her own kid, but one time before she lost custody she did send Killjoy to our house with a "It's funny Dad thinks he's in charge!" shirt.  She "worked" at a clothing store at the time, so no doubt she stole it from her employer.  We put Killjoy into a different shirt, and threw that one away.

You know, because it's hilarious to think a parent should be in charge of a 8 yo child.  PASinator extraordinaire.

Girl send it back to her!! Any gift she gives! Do not take that negativity and how you feel is completly normal. I read a few responses and like most said. She is trying to be relevant and in control because I'm sure she strives for that. If she was genuinely nice and meant a gift, in respect she'd hand it to you, but the whole matching the shirts thing was simply to poke at you. She doesn't have respect for you sadly so either you or husband needs to hand back any gift she gives this year. And like others said, still wrapped! Don't even give her the time of day to see what she spent money on. My husbands ex use to send Valentines, birthday, fathers day, and Christmas cards/gifts. Thankfully that stopped but girl we got to get that negativity away! They are toxic and disrespectful and you got to let her know you are unbothered by her craziness and hand it all back with a smile!

i would throw every gift from BM away, and I would have DH tell BM that gift giving to him would be innapropriate, and that his new wife takes the kids shopping for him, so she needs to stop.

BM did this when the kids were little little little, for Xmas, F-day, B-day. I didn't mind. For me it was not a big deal. It was maybe 1 little gift possibly two.  When they were older we ended it.

And then one day out of the blue she did it again when the kids were much, much older,

She bought a gift,  I mean the teen chillll-drennnnn dropped off a book inside a bag AND dashed off. 

The book was about men dealing with depression and thoughts of suicide.  I KID YOU NOT. WTH???

BM said the had NOOOOOOOOOOOO  idea what the book was about...yeah right. She is awful, just an awful person. Who does that? SICKO bm's do.

*disclaimer, of course my dh was not 'depressed with thoughts of suicide' 

You can ask dh to tell bm to stop because DH will handle kids and gifts. However,  If she really is just a nice person, unlike our bm and the book...it's polite to accept gifts. Once you have them it is up to you what you do with them. 

If this upsets you---by all means end the gift delivery into your home. YOUR home you decide what comes in and out. If kids are little little,,I would wait until they are a little older. JMO

...  for the first few years we were together. SS would bring them, specifying that they were to DH from his Mom. DH would place them carefully under the tree, opening them on Christmas morning in SS's presence, oohing and aahing appropriately, because we mustn't let the crotchling know they are no longer in a relationship where exchanging gifts is appropriate, you know? (As far as I know, DH never gave her gifts, though he did help the kid buy gifts for his Mom.)

The gifts to DH morphed from cutesy/passive-aggressive to sneeringly aggressive over the years. The year she sent DH a pair of pajamas and bedroom slippers I finally hit the ceiling. I made him send them back with the crotchling, although DH couldn't understand why I was being so nasty about his ex's kind gesture.

She never bothered again.

Make good use of the gifts to cause maximum offense. That T-shirt? Take a photo of you using it to clean windows with. Ensure the wording can be read. Then post abundantly on social media. 

BM had to look like she wasn't the one causing conflict, so she would send gifts with the kids, normally cheap chocolate that we gave the kids, one year was a garden statue (cheap) that mysteriously got broken after the kids left. She wrote it up in her affidavit as, "I sent gifts and he didn't even say thank you!"

As soon as the case was over, that was all done. The only thing she sends now are high conflict emails and demands for more money.

BM got a bottle of wine for SS to give me one year. I kept it.

1 year after my husband separated from BM she got him a mug "from SD (3 years old at the time)" that said "look Dad, I turned out alright". It broke while being tossed into the trash. (Rage over the divorce has now subsided)

I usually ask if SD wants to make something for her Mom for xmas, and she usually makes a Christmas ornament or something disposable I wrap up and put in her bag. I can guarantee it enters the garbage asap and I don't care. I would do the same!