Different admissions committees may handle things somewhat differently, as might different members of the same committee. However, I wouldn't worry about an 88th percentile score. As you say, it's respectable but not impressive, but that's OK. At top five universities, no score is high enough to be genuinely impressive by itself, and I don't think anyone gets that worked up about modest differences. (It's understood that some people are quick enough to score in the 99th percentile without breaking a sweat, while someone else might only reach the 90th percentile, and this difference is at best mild evidence for who has greater research potential.) At lower-ranked universities, there might be a little more scope for standing out via a high score, but it's certainly not necessary. I'm not aware of any university that would rule someone out for being in the 88th percentile (although of course I'm not familiar with every university's policies). By contrast, there are universities at which a 50th percentile score would cause consternation.
Of course, you'll have to have an impressive application in other ways, particularly letters of recommendation. However, you'd need that anyway: the extra margin of safety you would get in your application from having a higher GRE score would be small.
If you feel worried, it couldn't hurt to try taking the exam again. However, doing well in your REU and writing a great senior thesis are far more crucial than improving your GRE score, so you should definitely not compromise on those.
