For example, in X and Y there is a Celebi you can get from Pokemon bank. The Celebi has the move hold back, which is basically the same as false swipe. Anyway, if I were to make Celebi forget the move, would the move relearner let me reteach Celebi hold back?
Celebi was just an example, there are others like hold hands Vivillon too.
In Generation VI, any pokemom bred or obtained in a Generation VI game may also be taught any move it knew when it hatched or was obtained with. This includes Egg moves, Volt Tackle bred into Pichu, and Event -exclusive moves such as Pokemon Centre Tokyo Bay Happy Hour Inkay.
Same goes for Celebi too.
Source EDIT: Here's one for the event Moonblast Jirachi. Hope I helped!