I can't reproduce your issue on my system.
Here is what I get on my Windows 11 system with Fences v6. When I right click on the icon inside the fence. It open that icon right click menu. It did not open up the program on the desktop behind the Fence.
Added note: I also test the left click on the Wise Care 365, it simply open up Wise Care (not shown in the video)

Perhaps something else is interfering with Fences. Please do a Sandbox test and see it the behavior is the same as what you get in your system. Refer here for guide: https://support.stardock.com/space/SHC/1416560645/Testing+Fences+in+Sandbox. Try it and report back.
Thank you,
Basj,
Stardock Community Assistant