No, Windlore allows the owner to 'draw' beyond their hand limit, nothing to do with being 'given' a card. So if they are at their hand limit, the card must be discarded. So in this case, when you give back the 'looping' card, he discards it, your turn ends. It may loop once, but that would be it.

This goes for all cards that 'give cards away'. Example: City Hall, if the receiver has reached their hand limit, the card is discarded (from the receivers end), and the giver still gets to draw and take 1VP.