I don't have particular experience with either human nor exome sequencing, but I came across similar distributions in genome sequencing projects. Among others, I have observed it for a highly repetitive plant. In that case, the second peek corresponded to specific repeat class, that was really highly abundant in the data set.
Giving your mapping result, I concur, contamination is unlikely. So I would try to figure out from which locations of the genome these high GC reads derive and whether you can associate that with some useful annotations. Based on your mappings, you could extract regions from the genome with proper reads coverage, e.g. with bedtools, and than look for entire sequences or large windows of high GC.