There is a dilemma here regarding perception. What is a percentage in terms of how it is used in school grades?
To the technically trained, percentages are merely a notational convenience. As such, whether or not to use an article is unaffected by percent notation. The issue lies in the nature of the quantity being presented, not the notation being used to present it.
But with regard to school grades (and in a few other places), I think an argument can be made that the percent symbol is functioning as a unit of measure - and this changes things. Is 87 a quantity, or is it a quantifier applied to percent? Where do the attributes which establish the proper determiner lie - with the 87, or with percent?
My personal solution is to avoid using percent in situations where it seems to be working as a unit. I shift to a less confusing measure. I would say "scored an 87" in this case.
A percentage, a percentage point and a percentile are things, but a percent isn't a thing, and if it seems to be acting like one, the safe thing to do is swap it out. Once it is gone, the confusion goes with it.