I’ve had a couple of jute rugs and several pets so I feel your pain. But for what it’s worth, one of my worst jute rug staining episodes was caused by me and a full pint glass of water on my livingroom rug. Jute discolours if it gets wet, particularly the pale, pretty shades of jute.
How I deal with it, depends on several things. Is your room set up so part of the rug is under the sofa/bed? If so, just “spot” treat/wash the stained area (it will probably discolour) and then turn the rug around so the stained patch is under the furniture and the nice, original colour is out in the open.
I gained a nice bedroom rug after the pint glass of water episode - the livingroom furniture layout didn’t hide the stain so the water stained area is now under the bed in the guest room. No one will ever know.
But if the area is not hideable and basically fit for the bin, then i’ll take a chance and I’ll wash the whole thing outdoors with a hose. It’ll discolour, but the whole thing will discolour.
This has worked 50% of the time for me 😂
I use disposable cutlery to scrape off the solids and I found a good dry carpet cleaner which I use first. After that, I wet the whole thing down outside. The time it was bright, dry and sunny, it worked as the sun seemed to get the carpet back to its original colour more or less, but the other time I tried to do the same, it stayed water stained 🤷♀️
Im currently saving up to replace the natural jute with a ruggable version…
ps. The dry carpet cleaner works extremely well for spot cleaning cat/dog vomit but it must be treated quickly and only left on for 30 minute intervals, otherwise that can also cause the jute to discolour. Usually 2 or 3 rounds of 30 minutes and it’s fine.