cat choosing another home

Question
we've just found out that a neighbour living behind us has been welcoming
our cat into their home (they even have their own name for him!).  They have
a cat flap, so can't stop him coming in, but we are very upset that they are
allowing him to stay when he enters their home (they say he sits on their
knees etc).  Our cat is on dry diet food and I'm sure he's choosing to go in
there as he can get access to their own cat's food.  I'm really worried he will
choose to live with them over us, as they are providing lots of food and we are
the ones giving him the diet food (under instruction of vet).  He's a member
of our family and I'm very cross and upset that they are in affect trying to
temp him away from us.  I popped over and asked them to discourage him
from staying in their home, as he's on a diet but all they could say was "he's a
lovely cat and we like having him around"!  Thinking of writing a letter to
make it clear we want them to discourage our car from staying in their home,
so do you have some advice I can pass onto them on how to do this and what
we can do as well?

Answer
Hi Justine.  I'm sure this will be a difficult situation to try to resolve, even if you neighbor agrees to try to discourage your kitty from visiting so often.  Sounds as though he's found some food he's quite fond of!  Aside from shutting your cat indoors for much of the time, the only other thing I can think of that may work is to offer to replace your neighbor's existing cat flap with one that has an electronic lock on it.  Their cat would wear a collar that carries an electronic key, and the flap would only unlock when their cat approached the flap.  So your cat would be unable to get into their home.  It would be an investment you'd have to make in their home, but I think it would be least stressful on everyone.  It would be hard for them to have to continually shoo him away and create a state of unrest in their home, and it would be confusing to your kitty as well.  If this isn't possible, supervised outdoor time might be your safest option.