Well, for one thing, I don't mean any woman in just a towel is a tart or that wearing just a towel makes one a tart, but that if I were in the OP's position, that's probably what I'd be thinking about a woman trying to make it clear she fancies my DP.
But thinking about it, no I don't think I've ever wandered around the house in only a towel, in front of anybody I wasn't intimate with, not when lodging and not with lodgers in my house. None of the lodgers we've ever had has done so, either. I wouldn't go through my own house that I own in just a towel if I had visitors in, either. Nobody wants to see that! Everyone has always either worn a dressing gown or just taken a change of clothes in with them, or, if they forgot to bring something in, zipped back to their room. Does that make us all prudes?
To be clear, though, I never said or meant that the lodger is the problem, at all. Just as PP have said, the problem is him, not telling OP about female lodgers, happy to let them flirt with and fancy him, and playing at trying to get back together but definitely not walking the walk.