Op here. I am asking because my boyfriend's ex-wife keeps contacting him over what I feel is trivial, nonsense stuff. It kicked into high gear when bf told her we were getting more serious (even though she has a bf herself and was the one who left the marriage). I really want bf to tell her to take a hike off a short pier, but they do have minor ties through pets.
I am not even close to being a relationship expert but this would bother me. I wouldn't want my bf's ex calling him, unless it was important. If it is important, a quick email should suffice. My ex-husband's old girlfriend was emailing him regularly after we had moved in together (she initiated the contact after we moved in, not before, so it's not like they were in contact before I was in the picture) and while I didn't exactly like it, I was ok with it until she started telling him how much she missed him, calling him terms of endearment (including "love," etc), and telling him how there would "only be one of [him]" in her life. I think he was a little flattered and amused, but to give him credit, he did tell her to not contact him anymore. However, a few years later she moved back to town (she was now remarried) and she contacted him again, and this time she wanted to meet him. I reminded him of what happened earlier and the slippery slope she was on, and he agreed to not see/contact her. Well, fast forward a few months and her husband actually came into my work and yelled at me to tell him to back off and cut off all contact with his wife. I was floored. I had no idea they had continued the contact. Her husband showed me copies of emails they had sent back and forth. He had created a secret email address just to contact her. So, yeah... that was pretty much the straw that broke the camel's back. We were having a ton of difficulties by that time, so it was the sign I needed that it was over. We were married by this time and had a child, so I had a lot of contact with him after the divorce, but it was literally about our son and any finances we had. If we had not had a shared child, I would have been perfectly happy not to see him again.
My mom and dad were amicably divorced, and still talk often. Granted, a lot of it is about me and my sister and their grandkids, but he also helps her with items like her taxes, etc.
My old roommate was amicably divorced and they did not have any kids - she would text him or he would text her here and there to say 'hi,' but I wouldn't say it was regular contact. When she had to get new brakes for her car, he did help her financially. There weren't any other significant others at this point in time, though. She's now remarried and I seriously doubt she has any contact with her ex.
Wow, didn't mean to write a novel. As you can see, this is a subject that is near and dear to my heart. Good luck, OP, it can be a difficult subject. I guess my only advice would be to follow your instincts. If you think there is something behind her constantly wanting to contact him, there probably is. If the matters are truly trivial, your boyfriend should respect your feelings enough to tell her she needs to quit contacting him. Just my opinion!!