The phrase "to stop the itching" means to take action or use something that helps alleviate the uncomfortable feeling of itching on your skin. Full definition
To help stop itching, swelling and irritation, hold the cut end of an onion against the infected area for 15 to 20 minutes. (marthastewart.com)
I love it when an allergy dog stops itching with all natural, healthy supplements. (theblessedpetshop.com)
May it be to stop the itching in your belly, clothes for easier movements, or anything that will get you through the night, these pregnancy products are your best bet! (health-and-parenting.com)