I can't answer because have never seen it in Egypt, maybe I need to go more often! Egyptians opt for delivery more than drive-thru, I guess we're not the same car-culture!
In the purest sense of course:
الخدمة داخل السيارة
There are a very limited number in the UAE and frankly I've never really seen anyone use them. I don't really remember what the sign says, it was something like الخدمة في السيارة; I'll keep alert to the next one I see. However, I would like to suggest something like: خدمة التوصيل للسيارة, basing it on خدمة التوصيل للمنازل.