Without a picture of under the sink, it's hard to say if your aunt has room for an undersink RO system or how hard it'd be to install (and subsequently, uninstall). Even in the simplest case, with plenty of room and updated plumbing, RO systems need a supply line, a waste line, and a faucet, all of which a plumber would have to connect to the existing plumbing. Removing all of that when she leaves will be just as much work. Plus, if you had to install a new faucet, that may have required irreversibly modifying the sink or counter-top.
In any case, I really don't think your aunt shouldn't be doing any of this without permission from the landlord. If the plumbing fails and causes damage to the unit or other units, and it's traced back to the unauthorized changes, she could be in real trouble (disclaimer: I'm not a lawyer; that just seems like common sense). You might suggest your aunt talk to her landlord and see if they'll split the cost of installing a RO unit, in exchange for leaving it when she leaves.
Otherwise, I'd say go the counter-top route.