Is there a current court order? What does that say regarding contact? If not I might look if there is a local standard. 

In all likelyhood though is she likely to file the paperwork to take you guys to court over lack of phone contact? If not, then you could just do what you think is best for the kids.

Even if she does file, the judge will just order that you allow phone calls (if that is what they decide is appropriate) - then you'll just have to have them from then onwards. 

If the kids have therapists I might ask for advice as to how best to approach contact with their mother.

If there is nothing that says you have to provide phone access, I'd say you're legally clear to do whatever you think is best. If BM has an issue with it, she's free to file a petition for court ordered phone access.

That being said, I would be hesitant to completely block access unless it is upsetting/damaging to the children (meaning it's not just annoying to you - which I totally get why it is, I just don't think that's a good enough reason). That could easily be turned around on y'all in the future with BM telling them, "I tried to see you/contact you and they wouldn't let me!" 

Termination of parental rights is serious (as you know) and from my understanding reserved for the most egregious of deadbeats (severe abuse / neglect however your state statutes define it) or people who relinquish rights so someone better suited can adopt/provide.

With her calling (even every now and then) raises the question is she making at least some effort to be involved? Maybe she wants to take steps to be more involved? Or maybe she doesn't want to be actively involved just pop in say hi and go about her life? 
 

Whatever the case she deserves to be adequately notified her rights are in jeopardy to allow her to either challenge this or accept it. 
 

If I'm correct it will be very difficult to terminate moms rights (esp if she's not actively abusing/neglecting the kids to a severe level) if 1. She contests and 2. there isn't another parental figure ready to fill-in/adopt
 

*consult with a licensed lawyer 

I wouldn't block contact as long as she's not saying anything inappropriate (normally I would not say anything to the other parent but for someone who is about to be majorly reprimanded I would give them a final courtesy "warning"; I would check her on the phones like "look Betty, your kids are suffering when you inconsistently reach out and you need to be more consistent/active in their lives. Calling them every blue moon is not healthy so what are you going to do to improve this situation? What is the barrier to you calling them more regularly?") 

Like mentioned before those kids could figure out one day that you blocked their mother who'd been trying to reach them and they could resent you. You don't want to carry that weight on your conscience. Imo. 
 

*consult with a family therapist and attorney 

Your previous post gave plenty of reasons to be unavailable or at least have supervised phone calls with BM.  She gets not one private call with the skids and if she starts talking negatively, end the call.  Those skids need Dad to protect them as best he can from her. 
 

We went thru a time where our HCBM was acting the fool and we kept the skids until she snapped out if it.  ( funny how news of a new baby can do that to a HCBM) she threatened cops and the whole nine yards but DH just reminded her of her behavior in front the skids and she backed down.  They were shell shocked to say the least.  At least your DH has legal rights my DH didn't have.  
 

If she's so inclined to be a mother, let her initiate court.  I doubt she will.  

I agree with survivingstephell. Allow the calls but have them supervised. Don't allow private calls and end them if it turns negative

She knows if she does visitation, you will go after her for CS.  Making her pay the state,  and garnishing her wages.   She gets her pity calls whenD her guilt gets too much,    Agree phone calls if you allowed it should be supervised.

The big question is. In future years.  How are the kids /her kids view you blocking contact with there mother.  Some time maybe when the kids are youn adults. BM.will clam that she tried so much but tge evil SM block her efforts.   Don't put BM is goog light.  Tell the kids it's three weeks from last phone call. Ect.  
'AND  if the SK have a tablet. There's free programs like "text now ". That gives you free phone calls. Over the WI-FI.  Kids know this better then we do. 

I also agree with others.

Do NOT block the calls. NOR would I purchase a phone for the child.   

 The key is to give the minor child access to talk to her mom. Dads phone will be acceptable. -OR you could purchase a TRAC phone (dad controls access) no texting option. and tell mom here is the number to call the children. OR, use a land line. --

YOU, on the other hand  can block mom. I don't have a problem with that. The courts will not either.

Now about your lawyer and termination of parental rights IF IF IF mom does not see the kids by Dec. Just curious, what is the reasoning for terminating her rights?  

TPR. can take upwards of 2 to 3 years of court hearings when minor children are involved.. The court takes those matters very seriously and WILL give mom a lot of leave way starting with her first court appearance. 

Considering everything, and only from my view, let things be. Poking the bear could end up with a bm fighting this with a free lawyer for several years. She could be awarded more than you bargained for.  

I won't get into the mess that will occur if you and dh divorce. Are YOU willing to adopt dh's minor kids? Have you really thought about that?