No. This GPU is dead. You need to replace it.
Here's the guide to remove the motherboard so you can replace the video card. You can use lead or lead free solder. The solder will not affect how well the chip stays after replacement. Should you replace the GPU apply the thermal place correctly. I have seen the service manual archives from this era and it's disgusting. Apple pulled a DMCA though :-(.
MacBook Pro 15" Core 2 Duo Models A1226 and A1260 Logic Board Replacement
You can find Artic Silver 5 and Cooler Master High Performance thermal paste here. Please do not use the Apple thermal paste again. That stuff is garbage.
Just in case, read this on how to apply thermal paste if you need to. I'm providing it just in case.
Aanbrengen van thermische pasta