Well. Hm. I tried to think of a back from a logical stand point, but that didn't really work out well. :lol
I mean, it would stand to reason That up until our two universes took very, different paths, when Walter took Walternate's Peter. (Um, his son.) Things could have been very, very similar. There for the back of the bills up to that point might haqve been the same as ours, but to that point. However, I believe we already had a $20. bill by then, and he wasn't on it. (and never was, nor ever will be, since we have a cover boy for our $20. bill) Also, that looks like our more modern money, so it could have varied greatly from ours since Peter was taken.
And, seeing how we did see things in there universe, that indicate that things my have been very different then those in our universe long before Peter was taken.... Who knows what's on the back of there bills.
I mean, instead of the primed with the eye we see on the back of our Dollar bill, might be the "Stone Cutters" logo from the Simpsons, on there money.
Perhaps, something very close to our modern bills, but with just a few small tweaks. Like since everyone over there seems to answer to the Minister of Deafens. (or walt every Walternate's title is over there) In New York, more then the white house, in DC, maybe there more modern bills would reflect that. Then again, they may still have something to do with DC out of respect to what was. I don't know.
Really, as long as you don't step on the toes of what was been see so far in the show, or what we may see down the road, you could pretty much make up any history you like, to reflect on the back of the new bills. ( unless of course someone has a screen cap for the actual screen used bills that is.)
I mean, if "President King" is on the $20. bill, things have been very different over there since long before Peter was taken in the 80's