As PP have said, we really need to know if he's left it looking like a 4yo attempted to wrap a gift but nevertheless functionally adequate, or if he just didn't do it perfectly as "the work of a moment" with elaborate ribbon and scooped-in twigs and petals, like Rowan Atkinson's character in Love Actually?!
If it's covered and kind of rectangular-shaped (assuming the present is not awkward-shaped to begin with), and the paper is taped to itself, surely it's fine?
I have a family member who wraps gifts so that they look beautifully presented, with perfect sharp edges and corners; but every time, when you come to open them, you realise that she's achieved it by firmly sellotaping the paper to the actual gift - and the tape unavoidably rips the outside.
Thus if it's a box that will get thrown away anyway (e.g. box of chocolates or external packaging), it doesn't overly matter; but if it's a book, board game or similar, it spoils it permanently.
She's a very intelligent, highly-educated person, but no amount of 'tactful' comments - "Oh, what a lovely book - but what a terrible shame the cover is all torn now" - ever seem to get through. In that one respect, she's like Fr Dougal when you try to state a very obvious simple fact and she reacts like you're trying to explain trigonometry to a cat.
She either has a mental blockage in that one particular area or otherwise just doesn't care that people receive brand-new but already-spoiled presents, as she has indeed wrapped them and handed over an attractive (on the surface) package. I've never quite worked out which it is; but I'd gladly take non-neat edged messy paper over an actually destroyed gift any day.