Gilbert will stop, but only to find out where the cat went (because what if she took a shortcut to get the jump on him?!). He's immensely glad to find someone is preoccupying her now, and so he'll approach... and stop a good six to ten feet away from his savior.

"...Thanks," he starts, unsure how to say what he's thanking him for for until he just kind of lets the first thing come to mind slip off his tongue. "...for playing with her."