It is serendipitous that you mention those, as I have been thinking about finishing a short essay about those. To sum up:
Yes, there is significance to those. Although those colours are faded / distorted, those are the same crosses & context as found in other German dueling treatises (e.g. Talhoffer Thott-1459). The red cross on white is for Saint George (Joerg). The white cross on red is for Saint Maurice (Moritz). Each was a warrior-saint. So fittingly the knight would put a tabard or surcoat over his armour with such device for saintly protection, and to show serious intention, at the judicial duel. It could also be displayed via commencement banner or via (the hopefully unneeded) pall over coffin of the knight.
It may be comparable in its own way to certain headbands worn in context of Japanese dueling. Not to get too astray into their arts (and please let us not), but as I was instructed not to wear such in jujitsu, as such was still taken as saying "I am here to kill or die trying".
Likewise, I would assert that a similar gravity was meant by the German who showed up at a judicial duel decorated with either the Georgian cross or the Maurician cross. And accordingly, I would suggest that nobody modernly show up at anybody's training hall dressed as such, out of respect for peers and the past - unless that is what they actually intend (i.e. showing up so dressed at that one fencing studio near Atlanta GA).
I hope that explanation is of value.