Ask him about it ?

So my bfs ex is shady and constantly brings my name up.. i never had a problem with her but the disrespect only goes so far. I texted her and pretty much told her i didn’t appreciate the bs .. and she responded talking shit, in one of the messages she said “he will call me at work like he was doing”. She also had receipts to back up her statement. We have a pretty honest relationship but that doesn’t mean anything necessarily. She also mentioned he was begging for her days before their court hearing, ( she filed a false pfa causing him to lose his custody from the kids for a year), which i don’t believe he was doing but it makes me wonder.. would you ask your s/o if it’s true or not. I don’t want to start any problems, also due to the fact that this is a couple of weeks old but it crossed my mind