Hello, and welcome to Just Answer.
Your initial idea to use the warm wet washcloth was a good one, but it would be better if you could immerse your kitty's paws, one at a time (or all at once, if she'll allow) into a small amount of warm water mixed with a couple of drops of plain dishwashing liquid. Work on the paws to try to get as much litter off as possible, while it is under the water, then rinse very well to remove all soap residue, and dry. If someone can help you, and you work quickly, you shouldn't have too much trouble, even though she might not appreciate her paws being immersed in water.
Another idea is to apply a little mineral oil, vegetable oil or plain Vaseline to her paws, and this might help ease the clumps off without hurting her. To remove the oil afterwards, wash her paws with the warm water and dishwashing liquid, made to cut grease, and rinse well.
I hope you are successful!
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