Amazon's Buyer-Seller Messaging service is the only way you, the seller, can communicate with your buyers. Amazon is extremely particular with how its sellers use the service. It consistently monitors emails to catch sellers who are abusing the service. And if you are caught abusing Buyer-Seller Messaging, it could result in temporary email suspension all they way to losing selling privileges.
Using external links in Buyer-Seller Messages
Amazon wants sellers to contact buyers. You can email buyers to complete an order, respond to a customer service question, or ask for a product review or seller feedback.
With that in mind, you can't use Buyer-Seller Messaging for marketing or promotional purposes. When you email a buyer, your message cannot include:
Links to any websites
Links to Amazon detail pages or storefronts
Seller logos if they contain or display a link to the seller's website
Any marketing messages or promotions
Any promotions for additional products or referrals to third-party products or promotions
Amazon wants to ensure that the entire transaction and communication stays within Amazon, as explained in the first section of Amazon's Prohibited Seller Activities and Actions (found here). This means that the buyer and seller must commit to keep all communication with Amazon.
Use the Communication Center's email variables to ensure your message's links are following Amazon's Terms of Service.