to feed or not to feed visiting cat

I have a friend... no really, it isn't me... but my friend is being visited
by a cat who she said looked skinny when she first started coming around.
So she was feeding her and would let her in only to part of their house when
the weather was bad. She comes twice a day for food and always leaves at
night and sounds to me like she prefers it outside, but likes my friend as
she has left her dead presents on the doorstep. She says she otherwise
looks to be in good shape - just skinny.

All of a sudden the cat showed up with a collar on and a note attached to
the collar saying this cat doesn't belong to you so stop feeding it. So
now, of course, the cat is visiting regularly and deploying her best feed me
tactics which can be so hard to ignore coming from such a cute face.

What should my friend do? I want to say if the original owners cared so
much about what the cat was eating they wouldn't let it outside where she
can hunt and kill her own food. Or if there's a medical reason - that she
should only be eating a special food - again why let her live so much of her
life outside where she can eat plenty of other critters on her own. And
besides which, the cat is in my friend's yard - her private property. So
seems as though she could just as easily send a note back telling them to
keep their [un-collared until now so that no one would know if it were
stray, feral, or belonged to someone] cat out of her yard if they don't want
her to feed it. If they're so concerned about it's well being, keep it
inside where it will be safe from passing cars, dogs, foxes, diseases, and
good hearted people like my friend who are saving the owners some $ on their
cat food expenses.

But then, I guess if the cat can hunt as she's showed, then she can also
feed herself and maybe the owners wishes should be respected and she should
be left to be on her own.

In your opinions, how should I advise my friend?

Thanks,
Lydia