Wow, what spectacular fins! They should grow back no worries, but I would up your water changes a bit, as ammonia's the most obvious cause of little holes and thinning. In a 2.5 g tank, filter or not, I'd probably do 2-3 30% changes per week minimum. Fish with huge fins like that, I tend to do more.
The plastic plants might also be irritating them - can you swap them out for soft, silk ones?
I don't see any black on his fins, which is a good sign. If there was, I'd recommend salt as a first step cure. But I don't see it so I recommend a couple of major water changes with a good gravel vac, and then just trying really clean water for a couple weeks, as long as he stays healthy in every other regard. The new growth will look pale, sometimes a bit spiny at the ends as new rays grow in.
If that doesn't work, or he starts to look poorly in general, it may be something more serious, but for now, that's what I'd do.