I escalated this to the relevant engineering team in charge of the Dropbox web site. They reviewed this and unfortunately they're reporting that we can't offer a fix as this is only occurring in unsupported browsers.
It is important going forward that you use officially supported browsers/versions, for the sake of compatibility and security, as web technology and dependencies evolve over time. You'll need to ship an update with a supported browser to in order to maintain compatibility with the Dropbox web site.
My apologies I don't have a better solution for you!
