There is no need to use dt for that because you want to set it's position once (to self.y - 1080) - not move to position (by dt).
So if Tile_bg have reached target (Y>960+Tiles_Bg.Height/2) then it will jump to self.Y -1080.
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Rory - this is the closest i've gotten, adding in margins which are set based on the speed of the game.
dt gaps