Some recent security changes in OSX 10.9.5 and 10.10 have caused some issues with the initial launching of TechSmith Relay, resulting in this error message.
First please go to System Preferences and then click on Security & Privacy
After that you will want to click on the lock in the bottom left corner, and then make sure Allow apps downloaded from: Mac App Store and identified developers.
In some cases you will see the option to open anyway during this step.
After that please go to the Applications folder and right-click on the TechSmith Relay.app file, and select Open from that list. You will see the same message, but will have an "Open" button to allow TechSmith Relay to launch.
This issue has also been resolved in the latest release of TechSmith Relay Recorder. If the TechSmith Relay server is on 4.4.2 you should update to the newest version of the recorder when possible.