Kill it. Vinegar is an acid and can kill anything it comes into contact with. I used it last year to kill off my back yard lawn before reseeding.
Vinegar will definitely kill the grass. I know this because I use a 1:1 vinegar to water mixture to kill weeds. It can't distinguish between them so it kills all of it.
Vinegar will kill it. Vinegar is the main ingredient in homemade weed killer.