It could just be a literary red-herring (hmm...is that a term?
) used by Tolkien to justify the Eagles insertion into the story. Tolkien calls the Eagles "dangerous machines" that have to be used sparingly, because they are servants of Manwe, and having the Eagles constantly get Gandalf out of tough situations is cheap writing.
Maybe Tolkien just wrote an unexplained "debt" Gwaihir owed Gandalf, to somehow justify Gwaihir's timely appearances and rescues?