Doesn't sound like there is any need at all. 61C is practically chilled for a GPU. You must not be asking much of it, or it has a very good cooler on it.
Even water cooled and overclocked my 1080 will still hit 55C at full blast. I would expect it to be riding it's throttle point, usually 83C. ASUS and others sets theirs to 73C sometimes to keep the card silent.
Air is an insulator, the purpose of thermal pads is to remove that air gap and connect things that need cooling to parts of the cooling system. Once they have been squished down they tend to retain the shape of what they were in contact with, kind of like, gum?, or a dense foam. So when you place them back down you just want to try and make sure to get them back in the same places and not have dirt, debris, etc trapped under them. If they are misaligned those little pockets of indentation will not help in the cooling and trap air between the component and cooler. The pads tend to stick to either the card or the cooler, just transfer anything that came off with the cooler back to the card before reapplying paste and sticking the cooler back on, should get the best results.
If they tear, not the end of the world, as long as the majority of the chip or component in question is covered, should be okay. Aside from the VRMs, which can often operate up to crazy temps like 130C, most things don't need a whole lot of cooling. Memory is capable of getting warm, but if it is an axially cooled card, usually no big deal. Blowerstyle, it kind of matters since there is no direct airflow.