According to the Bastet Book, page 98, Cheshire Prank foils even magical perceptions. Note that this means after the character has faded from view. Until that time the gift can be countered as any other. Once the Gift is in effect, the character using it cannot be located exactly, but the character’s presence can be noted in the general vicinity (up to the Judges) by magic or regular abilities, such as if the Bastet makes a sound.

Furthermore a judge may rule if abilities say something to the effect of “May see through any illusion, Obfuscate, Invisibility, etc” that the character may attempt to roll against the successes scored by the Bastet, remembering at least, that this form of invisibility is supposed to be complete and not able to be discovered by magic (make it an appropriate test).