Final update: the broken logo image is no more. I finally tracked the faulty html down to the Weaver Xtreme theme settings and removed it once and for all. Goodbye, little question mark.
Update (2/26/17): It turns out that I did have uses for several of the GDAL 2.1 features, and there was a simple fix for the problem — switch to a different distribution. I tried the GIS Internals msi installer and everything worked the way it should.