I am sorry to hear about your newly adopted older kitty's habit of eating cat litter and now eating poorly in general.
She may have some mouth pain, but eating cat litter is often a sign of a serious underlying disease process.
Eating non-food item is called pica.
Ideally she would see a veterinarian for an examination and some blood tests including a complete blood count, biochemistry profile, thyroid level (T-4), and feline leukemia and feline immunodeficiency tests. Some cats exhibit pica (eating or licking/biting non-food items) when they are anemic or sick and we do want to make sure that she is healthy and there is not a physical reason for her behavior. She could be anemic, or suffering from metabolic organ disease or an immunosuppressive virus. This can also be a sign of nausea.
At home to try and settle her stomach in case this is related to nausea you can give either:
1)Pepcid ac (famotidine) at a dose of 1/2 of a 10mg tablet per 7 to 20 pounds of body weight every 12 hours
2)Prilosec (omeprazole) at dose of 1/4 of a 20mg tablet per 7 to 20 pounds of body weight every 12-24 hours
These are acid reducers and could help her feel less nauseous, and thus less likely to chew/lick on non-food items. These medications are quite safe and can be used for several days if they help her feel better.
To perk her appetite and ease nausea while you are waiting to have her examined you can try offering a bland diet of 2/3 boiled, minced, white skinless chicken or whitefish and 1/3 boiled, white rice mixed with some low salt chicken broth to make it easy to lap up and swallow and get additional fluids into her.
Given her age, poor appetite and this behavior though she should see a veterinarian for diagnostic testing as soon as it can be arranged.
It has been my pleasure to help you today, and I hope that I have earned my 5 star rating. Please remember to rate my service by selecting the 5 stars at the top of the screen (rating me now does not close your question). You are welcome to ask follow up questions about my response here until you are satisfied, simply use the reply box and let me know. Thank you!