If they're frayed from the plastic plants, then you probably don't need to medicate... although keeping the water crispy clean certianly wouldn't hurt.
Here's what I'd do:
Remove the plants, and test them to see if they're sharp. If you have panty hose handy, run it along the edge... if it snags, it's not a good betta decoration. If you don't, run your finger along the edge, if it's sharp, it's not a good betta decoration.
There are people out there who can, and do, use plastic plants. Most people can't though, and that's why we recommend silk or real plants.
I suppose if you have fine grain sand paper or a nail file, you can also gently dull the edge, too.
Since a cut betta is obviously more vulnerable to infection, make sure you keep up with water changes while he heals, and keep an eye on his finnage... it
could be finrot, but it sounds like a tear to me.
They heal pretty quickly, given the chance.

Don't sweat it.