I don't know... It's a very tricky situation! Depends on a few things, I guess, like what the credit limit on the card is. If it was low, I would probably let it go.
I would probably bring up at some point with H that since we're both liable for all debt incurred by the other person, even if it's just in one person's name, there needs to be transparency and trust on both sides. But the timing would have to be chosen very carefully... Sometimes I'm indirect with H on difficult issues, I'll mention a similar situation and leave it to him to see the similarity with ours.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17