Mysher, I know the block by other names but is this the Scrappy Duo by Fons and Porter? I did a little searching and looking.
I was thinking that maybe if you haven't put the blocks together yet you could add another border around the blocks to add more contrast or to fade out the background a bit more. Either another mitered edge or a standard lattice. Obviously you will add to the size so figure out how many blocks you have to mess with first.
Otherwise, if you really want to fix the project, taking off just the background triangles from the blocks and replacing them wouldn't be so bad. Sometimes a little portable project while you are watching tv or waiting is actually sort of pleasant.