Turns out that it's more complicated. It's not a Flash part of the homepage but it is somehow dependant on it.
I discovered that at least one button shows w/o Flash, if you are not logged in.
On mobile (via browser) ...
and on PC:
Once you log in on mobile, it disappears, as it does on PC without Flash:
(Apparently, my picture host postimage has been hijacked by a rogue invader. Looking for a new provider with direct links)