Final answer:
RD Gateway is the role service that enables users with Remote Desktop Connection client to connect to an internal network over the internet securely.
Step-by-step explanation:
The role service that allows users with the Remote Desktop Connection client and an internet connection to connect to an internal network is RD Gateway (Remote Desktop Gateway). RD Gateway uses the HTTPS protocol to create a more secure, encrypted connection, allowing remote users to connect to internal network resources without the need to set up a VPN. It also helps manage the connection and the resources remote users are allowed to access, using policies such as RD RAP (Remote Desktop Resource Authorization Policies) and RD CAP (Remote Desktop Connection Authorization Policies).