How do I correct free-standing deck moving away from home?
This is one of the reasons free standing decks are not a good alternative to a deck that has been engineered, permitted and structurally connected to the house.

Using the house to fix what is, essentially, a foundation problem with the deck will not necessarily go well.  It is not likely that all parts of the deck moved away from the house equally (structures don't usually "slide" around.)  It is more likely one side has dropped opening a gap on the house side.  This is common, and can usually be fixed by jacking the outside edge back to its original position.

Worse case you will need dismantle and rebuild the deck, sitting it on proper foundations constructed below the front line, and anchoring it to the home's rim joint.