Work against gravity confusion

Hi I've just started learning work, energy etc and the first question in the book is in the form:

An object of mass m is lifted by a tension through a displacement of h. Find the work done on the object.

I know that the answer is simply mgh J, there is something that I don't quite get.

Why can't it be that the tension could be greater than mg but still lifting the object the same distance (in less time) so therefore does more work? I hope that makes sense.

Thanks :)