I have a Zotac 780: http://it-review.net/uploads/images/Article/2008/zotac/Zotac_GTX_780_AMP.jpg On the rare occasion, the left fan will start whirring. It'll only be when I'm not playing anything and when it's cold enough (it'll only ever happen early morning or late night). I usually 'fix' this by pushing it in a bit but I know over time it'll get worse. If it eventually becomes noisy all the time, should I just take it off? If that's even simple, as I know it could be replaced with another (I now use a fan from a case fan for my CPU cooler) but that it's a bit complex and MacGyvering. I bought it here in 2014 so returning it isn't an option, not that it seems worth it for a fan anyway.
Remove it, look at the model number on the back of the fan hub, search for a replacement on ebay/aliexpress.
This. One of the fans on my Zotac GTX1070 started making a rattling noise on startup for a about 30 seconds on cold mornings, I searched for the EXACT part number on AliExpress and bought a pair for about £10 delivered. It said it would take 20-40 days to arrive, it got here in 5. Just make sure you get the EXACT same part number that is on the back of YOUR fans, don't rely on guessing via Google, there are many, many variants of fans with almost identical parts numbers.
Treat the ball bearings in the fan to a little fine machine oil! Should only cost a couple of pounds from ebay then the smallest application can fix many fans. Usually you just need to peel back the sticker to get at the fans core. Depends on the fan though!