What causes a grinding or scratching noise when shifting from 2nd to 3rd Gear on a 2000 Celica GT?
I did have my mechanic add some gear oil but was thinking maybe I should have him drain out old fluid and put in new gear oil all together.
tl;dr: There is an excellent chance that replacing the gear oil (or even replacing it with a different product) will get rid of the noise.
A minor grind or scratching sound in an older gearbox is almost always a consequence of worn synchromesh gears. The fact that these pieces get worn / consumed over time shouldn't be too surprising considering how much work we ask them to do.
However, there are measures that you can take to improve the situation. One of them is to do exactly what you suggest: drain the transmission fluid and replace the whole load. If your gear old is also aging, it is likely not doing the best it can to lubricate the moving parts involved in synchronizing those ... synchromeshes.
However, you can also go a step further and investigate a different formulation of gear oil. In one of my first questions on the site:
I posed the question of whether an alternate product would be suitable for an aging gearbox. The product had a reputation of trading quick shifts for smoother shifts (i.e., no grinding shifting third to fourth gear for me).
After 70000 miles of personal testing, I can tell you that, yes, this product works for me.