Hi,
There is somthing you can try, as you can tell once the carpet has been bleached the colour is gone for good. My Mum cats were bringing in red mud on there paws and leaving red dots on her grey carpet and there was know way of getting the stains out.
What I did was carefully put bleach on the stained red paw marks to remove the colour, then bought fabric dye the closest to the carpet colour mixed a small amount with water and carefulIy put it on the carpet and blended it in with the rest of the carpet.
If possible try it out somewhere on a piece of carpet where no one can see it so you can work out how weak or strong to mix the fabric dye.
It work out great for my Mum, you can’t see the stains or where I had to bleach the carpet. Hope this helps you out. Noelene