First you got to figure out how the grease is getting out from inside the boot. If the boot is split, you have to replace it… That means either a new half shaft or some serious wrenching if you want to just replace the boot.
Since you have grinding noises during turns however, and you’ve already established grease is leaking out from that boot, I think what I’d do in this situation if it happened to my Corolla is to remove the outer CV joint from the shaft and inspect it on the bench. If there was any signs of the ball bearing or race damage, I’d replace the joint. If the surfaces looked ok but the grease was dry I’d clean everything up and install new grease and put it back together. On the Corolla anyway that’s a relatively easy job, since the entire shaft doesn’t need to be removed to just remove the outer CV joint. On some vehicles however this isn’t possible, or at least not very practical for a diy’er. For those vehicles it easier to remove the entire shaft, which is then usually just replaced with an aftermarket rebuild shaft.