Back in the 1940, 1950s, perhaps as early the 1920s, and into the 1960s, a grip was a suitcase, satchel, overnight bag, etc. In a sentence, "Gimme an hour. I'll pack my grip, meet you at Union Station, and we can blow this joint!" Today, some people still use this term to reply to a clothing bag of some sort, but I suppose it could also refer to a book bag, duffle bag, etc.
"Here you go, Joe. Can you put my grip in the overhead?"