Solved
Warning: Emblems cannot be removed.
EA help has advised me that, somehow, it is in fact the case that it is not possible to ever remove an emblem once you have selected one. You can change to a different one.. but there it is no option...
Forum Discussion
Are you perhaps part of a clan? I remember a time where thr clan leader could override everyone else's emblems (and even give all members Dice Friend or similar if thry themselves earned it).
You always have the option of turning off all UGC but that will affect everything
