AWS support for GRE in site-to-site VPN connections.

You can use Transit Gateway Connect attachment if you want to use GRE tunnels. Also, keep in mind GRE encapsulates the traffic, it does NOT encrypt the traffic in transit, so if you need secure connectivity channel then you should look at implementing IPSEC instead of GRE.

You can create a transit gateway Connect attachment to establish a connection between a transit gateway and third-party virtual appliances (such as SD-WAN appliances) running in a VPC. A Connect attachment supports the Generic Routing Encapsulation (GRE) tunnel protocol for high performance, and Border Gateway Protocol (BGP) for dynamic routing. After you create a Connect attachment, you can create one or more GRE tunnels (also referred to as Transit Gateway Connect peers) on the Connect attachment to connect the transit gateway and the third-party appliance. You establish two BGP sessions over the GRE tunnel to exchange routing information.

Reference: https://docs.aws.amazon.com/vpc/latest/tgw/tgw-connect.html

Take a look at these blogs:

https://aws.amazon.com/blogs/networking-and-content-delivery/simplify-sd-wan-connectivity-with-aws-transit-gateway-connect/

https://aws.amazon.com/blogs/networking-and-content-delivery/integrate-sd-wan-devices-with-aws-transit-gateway-and-aws-direct-connect/