Laptop fan at max cooling after I removed its GPU.

The first question is whether or not your laptop has two fans or just one? The answer is probably going to be the same either way but with slightly different reasons and results.

If the unit has two fans, one for the GPU and one for the CPU, and the GPU has been removed, then there is unlikely to be any sensor data available to the hardware in order for it to determine whether the GPU is getting hot, so it goes to full fan to be on the safe side. If there IS a fan for the GPU, you can likely unplug it for now. This will require some disassembly but since you've already removed the GPU I think we can assume that you're either comfortable with that or know somebody who is. There always remains the possibility that the BIOS expects to see an RPM reference signal from the GPU fan and won't boot if it fails to see that signal, as is often the case with CPU fans.

If there is only one fan you are going to just have to deal with it as the laptop is unlikely to boot with no reference signal from the fan plus your CPU would overheat without it.

I don't think it's likely that anything will be harmed by allowing the fan to run full speed aside from being a nuisance to your sanity and a high draw on battery power. Hopefully this is only a temporary condition and you will have the GPU back in before long.