When you are using your RDP in a public computer, its not really safe to let others see how do you use the computer or which websites have you visited. The same is for your remote desktop, its better to clear any history of your works. These are simple steps to remove or clear the drop down history of windows remote desktop default program.
First you have to remove the “Default.rdp” from your “My document”. It’s a hidden file then you will need to enable showing the hidden files within folder option.
The next step is removing the related key from Windows registry tree. From RUN (Win key + R) type “Regedit”, you will see the Registry tree , navigate to HKEY_CURRENT_USERSoftwareMicrosoftTerminal Server ClientDefault
Here you can see the keys related to your RDP, just remove it and you are done.