If it was me, i'd do one of two things:
either get out a paint brush and paint myself a stripe with a dry brush edge, and import that into illustrator for the rest or...
switch over to photoshop, get a grunge brush that you like or make one yourself, and either brush out the area in photoshop or recreate a similar look in illustrator and use an opacity mask or the divide function to get the look you want. The problem with doing it in illustrator is that it will not look very realistic without quite a bit of work, much easier in photoshop and then import the image into illustrator for the rest of what you're doing.
I mean, they have grunge effect brushes and stuff for illustrator but.... they LOOK like you just applied a brush stoke, and that looks goofy usually.