How to Hide Origin of Outbound Traffic

I apologize for my lack of knowledge on how the intricacies of the web work ahead of time.

I run a fairly large dealsite (lets call it dealsite.com) and we send a lot of traffic to Amazon. Is there anyway for me to hide from Amazon that the users are are coming from dealsite.com? I do not want Amazon to know that we (dealsite.com) are the ones sending the traffic.

Maybe strip certain cookies? Send outbound traffic through a proxy?

I am not doing anything illegal and these are real users not bots.