Can my ex do anything?

I dated my ex about a year an a half ago now and I'm seeing someone else currently. My ex and I ended on good terms, it just wasn't working relationship wise so we decided it was better to just be friend's. Now while we were dating I had some health issues and needed surgery etc. So, he offered to pay my rent for me and a couple other bills for the time being. I never ever asked for the money, he just offered, pulled it out of his account and handed it to me. Now he has a new girlfriend and she has it stuck in his head that I stole the money and he can now take me to the cops and/or to court. I have his number blocked on my phone as he kept harrassing me for it and he also messages my mom. My current boyfriend and mom both say if he does take it that far there is nothing the cops or court will do because he offered the money, it's been awhile since this happened, and there is no legal papers signed by us. Are they right? What can happen?

Please serious answers only!