Thanks for the replies.
@SoCal App: Yes, it was inked prints and not a live scan. After the first card came out a bit smudged we did use alcohol swaps immediately prior to the printing for all subsequent cards. However, even with this, the prints were still not very clear and even to the untrained eye (i.e. mine) the prints were quite hard to make out for some of the fingers. We also tried using some of the retest stickers as apparently this can make a difference sometimes but it wasn't much better.
I might get lucky and they might get accepted anyway. If not then I guess I could always risk going to the US and doing the prints with live scan prior to commencing training if there is a chance that this is less subject to quality issues. I will do some research on this just in case as it will obviously be very annoying if I go all the way there and still can't get TSA to accept the prints. At least I will get a nice holiday out of it I suppose
@IO540: Thanks for the suggestion but I guess my original post should have said "legal work around". If I can't for any reason do the training in the US then I will just do it in Europe so it is not the end of the world and is not worth risking the wrath of the US government by trying to bypass the proper processes.