Is it permissible for me to take a portion of the commission I receive for affiliate marketing and give it to the customer to encourage them to buy through me?

This work is not marketing for products that would entitle one to a commission, because the questioner does not benefit the company nor bring new customers, and his work is limited to benefiting himself. If this understanding is correct, then this method is considered deception and does not warrant a commission. The questioner can review the company and inquire about this scenario, and if they permit it, then there is no harm.