(US) Can shady merchant dispute chargeback if they shipped (unwanted) item after credit card gave me back my money?

Hi r/personalfinance, I don't usually post here but I didn't know where else to ask for help. Didn't want to go directly to bank in case it screws me over. So a while ago I ordered an item online from a smaller (and now clearly less than reputable) company. After placing my order I received no updates from them on the matter even though they claimed 1-3 business days for shipping. I contacted them several times trying to ask for updates and eventually started asking for refunds. They didn't respond to a single one of my emails and I suspected I had been scammed. After over a month I decided called my credit card company to file a chargeback which I fortunately won and had my money refunded.

Now without my knowledge the company ships the product and it arrived at my home a couple of days ago. Their excuse was they didn't get my messages (yeah right). I told them I didn't want their product anymore but they won't let me return it. They keep telling me (rudely) to cancel the chargeback and pay them money again.

If they contact my bank and tell them they shipped my order will my bank take the money from my account again? Could this have possible negative consequences for my credit or financial standing in the future? Can I just ignore this P.O.S. company and their demands?

Thanks a lot guys!