If a character with the utility belt loses the Gotham Knight team affiliation, do the lose the utility belt or does it say cause it's only checked when it's equipped .

it only checks at recruit

actually its checked when you attempt to attach it to a character.

you cannot even transfer a Utility Belt to a character without the G/K team affiliation.

but if you already have it attached legally to a character, and that character looses the G/K affiliation, then the Belt will stay where it is.