What are you using it for? I've got a really good solution that would probably be perfect, but if this is a special currency note, I'd try it on just a plain dollar bill or something first to make sure there are no problems.
First, you can theoretically iron something like that if you put a pillow case under it. My other solution would be methyl cellulose, which isn't the easiest thing to find, but certain art supply stores have it. Generally it's not at a place like Michael's, but Dick Blick's would have it, and some specialty art supply places would as well.
Methyl cellulose is used in book repair, but I use it personally to strengthen and stiffen tissue papers for origami. It works amazingly. Essentially, it comes in a powder form, and you mix a couple of teaspoons with a cup of water and mix it very well (this takes time, and I use a small hand coffee stirrer because the mixing is the hardest part, honestly). Make sure the cup you're using is very clean, btw. The consistency you want is about that of egg whites, so usually you just add more in bits until it gets to the right consistency.
Once it's mixed pretty well, you want to let it sit overnight to really make sure it's properly mixed. It will usually feel a bit thicker and after a stir has a better consistency. You just don't want pockets of white stuff in it still.
Once that's done, put the paper you're working with on a piece of clean glass. Now, bear in mind that the glass-side of the paper might end up with a bit of shine to it at the end of this process. You also want to do this on glass because methyl cellulose is essentially glue, and if you put it on anything other than glass, it's going to stick. Personally, I use my patio doors because they're big enough for big sheets of paper, but really anything glass will work. Also make sure you use a very soft brush to paint on the cellulose because stiff brushes catch the fibers of the paper. I always get the softest thing I can find at the art store and am just gentle with it.
Once it's painted on, let it sit until it's completely dry. If you try to peel it off too soon, it can harm the paper, usually warping it or causing it some odd stretching. Once it's dry, you can very carefully peel it from the glass. I say be careful because depending on how thin the paper is, the edges might be a bit tough to get off, but generally speaking it just comes off very easily.
This works really well for removing creases and smoothing paper out, and it also makes it stronger so it's less likely to be damaged in the future. It's a bit of a process, but for what you're trying to do, it might be your best bet. Just make sure you practice on some different papers first so that you get an idea of how to work with it before you try it on anything precious.
ETA: This would work really well, but because it leaves it a bit shiny on one side, you might have an issue with someone thinking it was counterfeit. I'm also not sure how the counterfeit checks work on a treated bill.