It doesn't just apply to paper money either; "In God We Trust" appears on all modern United States currency. Its first appearance on money came around the same time "under God" was inserted into the Pledge of Allegiance, and presumably for the same reasons.
And it should be removed...well, not from circulating currency, of course. But new issues should omit the sentence, in which case it would only take a few years for it to be gone from new currency altogether. New coins are issued every year, and new paper money is issued each time the Secretary of the Treasury (the year of issue on the note changes) or a new Treasurer is appointed (a letter is added to the year of issue, e.g., 2006A, 2006B).
But the politicians don't want to remove it, just like they don't want to remove "under God" from the Pledge. The vast majority of them are Christians; they choose to allow this infraction simply because it suits them personally, not because it is a sound practice or in line with the basic principles of secular government.