Yes, it is possible for customers to reject the gift; however, this can only be done if the “Compatibility with all discount types” is enabled under the Discount Codes Compatibility settings:
Compatibility with all discount types
If a customer changes their mind and would like to decline the gift that was automatically added to their cart, they can simply click the remove button on the cart page.
However, if they decide to keep the gift right after removing it, they would have to clear their cart and then re-add the items to receive the gift again.
For Free Product Choice gift offers, customers do not need to select anything, so no gifts are added to the cart.
Compatibility with discounts coupons only (draft orders)
Since this option uses Draft orders to add the gift, customers cannot reject or remove the free gift. If a customer is eligible for the free gift, they will always receive it. However, if the gift offer is set as a Free Product Choice, customers should not select anything, so that gifts are not added to the checkout page.
For more details on the two methods of adding free gifts to the orders, please check out this article.