If your husband has other nicer items from his mother that are not old towels that you don't mind keeping around, then no need to hang on to the towels. If this was the last physical reminder, I'd let it pass.
No, believe me, it's NOT the only physical reminder. If it were, I would have never even bothered to get them out of the box. The house contents were divided among the 4 siblings. Add to that, she was an artist, so there were >200 paintings/drawings/sketches that had to be divided among siblings and grandchildren. I've got 6 nudes she did (2 are hanging up), as well as portraits and still lifes all over the house. We've got silver, china, you name it. Wicker chairs, books, magazines.
She never threw anything out either, so when she died, the kids had to do it. Same with my parents. When we moved into an unattached house after 22 years in a townhouse, I had to somehow blend 4 houses into 1. And I'm still trying. That's why I said, you simply can't keep everything. There's got to be a line in the sand somewhere.