This is definitely not shirk. It’s seeking blessings of Allah through Hazrat Abbas’s loyalty and sincerity. Kindly explain to them Allah is the main source of blessings and thread is connected with someone who is highly blessed by Allah. Hence, you have it with you.
If they insist and you realize it’s causing fitna in the marriage, there is nothing wrong in removing it and put it either in your wallet, purse, hand bag, pocket etc