If anyone pays the medical bills on their behalf that person can claim the tax relief.
Re the covenant you need to be careful if they are on a non contributory pension that you don't affect the amount they are getting as the non contributory is means tested. The benefit of a covenant is that as above poster says they can claim back the tax you paid on it, so if you covenant 2k to them each year, then you actually give them €1,600 and they claim back the €400 standard rate tax paid. If you are a higher rate taxpayer you can get some extra relief too.
Biggest problem there though is if the pension is affected by the amount of extra income.