It's completely ridiculous - don't pay it. Yes, they should have a communal (ARC) license but in any case, this sort of thing should be included in the weekly fee - it's hardly an 'extra'. (Actually I think they've got a bl**dy cheek.)
If you work out how many residents there are and multiply by £7.50 per month you'll see what they are making. Ask them to justify it.
Moving into supported living, sheltered or care home accommodation? Taking your TV? Don't cancel your licence - move it to your new home. Find out more.
www.tvlicensing.co.uk
Just to add, my mum was in a CH for 3 years but was never charged tv license fee.