Brick veneer falling away from house
The idea of pushing a brick veneer wall back onto its bearing surface is really not a good idea. Besides water will not push it off, something else did in my opinion, like wood that swelled up from the leak, but that will be minimal. I would still be more concerned about the water around the framing behind the brick. If the brick ain't fallen yet, it may not. But it may need to be taken down to repair the band joist, plate, perhaps. Then set the brick back with proper waterproofing in place so when water gets behind the facade it won't matter. FWIW, in a building science seminar I attended, the speaker Joe Lstibureck, discovered that brick allows 10 percent of the water that hits/saturates the surface to pass through its thickness to the what is a hopeful moisture barrier behind the brick, in front of the framing...