frequent water changes are the best thing to help them grow back. For a 1/2 gallon, you should be doing daily water changes anyway, or at least every other day, so that should be all you need if it indeed was the plant that was causing it. Do you notice black or red around the edges? If so, he has fin rot which needs to be treated with daily changes and possibly aquarium salt. It's also possible he was biting them.
P.S. Just to warn you, most of the people here, including me, feel that a 1/2 gallon is way too small for a Betta - so be prepared for that. The general rule for all fish is 1 gallon MINIMUM per 1 inch of fish - so if your fish is 2 inches long, the MINIMUM size tank you would need is 2 gallons.