I would offer to the neighbors payment for the food etc they
invested in the cats. If you feel awkward, send them a letter.
That might mend things a bit.

I am so glad for you that you are resolving this. We have a thing we do, called "treat time" so that our cats will come to the special treat (very special treat) in an emergency.

Maya gets shrimp.
Weezie gets Fancy feast crunchies or chicken. Or tuna for both.

They get a little bit each day anyway...as a reward for being called. They will run to me from the basement or attic when I call their treat time.

Little Houdini, didn't seem to come well when called. But she did do well for about 30 days, with some training outside each day.
So I didn't worry about her. I have never had such a painful event with our cats, who always went outside too. You can see some of their photos in my album on my profile page. She was raised completely outdoors at the farm setting where I answered her ad. She learned the litter box in one day and was a polite kitten...like she had lived in a house all her life. She was never "wild". I never expected her to disappear therefore!

This is the photo I used to show people when I was looking for little Houdini... I even went to the voting in Nov and showed everyone there waiting to vote! I still grieve for her after 2 yrs. I feel it is all my fault.
.
I still hope she is alive and happy in a new home.