Final answer:
The most likely technology being used to provide access to the third-party company is RDP (Remote Desktop Protocol).
Step-by-step explanation:
The firewall change implemented by the security administrator suggests that the company is using RDP (Remote Desktop Protocol) to provide access to the third-party company. The specific ports mentioned in the firewall change (80, 636, 5800, and 1433) are commonly associated with different services. Port 80 is used for HTTP, port 636 is used for LDAPS (secure LDAP), port 5800 is used for Virtual Network Computing (VNC), and port 1433 is used for Microsoft SQL Server.
Therefore, based on the given information, the most likely technology being used to provide access to the third-party company is RDP.