"How? What were you even doing out there anyway?" Give him one good reason to believe it's actually different and perhaps Oz will refrain from sneaking out of the house.

Or just take Jack with him.

Or Oswald for that matter. There's any number of people he's sure he could convince to be his bodyguard for a day or an evening. Just not Gil. Because he's a stick in the mud (and considering Oz just mentioned Oswald, that's saying something).