Notsafeforkids

I just found this menu called Accessibility button. There's an option to remove all overlay icon without turning off Accessibility permission and break the app. Problem solved for me.

I think I just found the root cause: KSK engineers made wrong/incomplete accessibility permission. I uses KSK premium version. First of all, there's 2 kinds of Accessibility permission: The main permission that must be turned on for app to work properly and the "shortcut" permission to display overlay icon which function is to easily turned off and on the main Accessibility permission. On my Xiaomi Redmi Note 10 phone MIUI 13 OS (Android 12 based), I used Kaspersky Antivirus that also required Accessibility permission. The difference with KSK is that Kaspersky AV separated between main Accessibility permission and shortcut permission as shown in my screenshot. Did you see the two ugly overlay icons over there? The overlay icon for Kaspersky AV also can't be removed/turned off with the method @Flood and Flood's wife suggested, same as KSK overlay icon. However, I can remove it by turning off Kaspersky AV shortcut Accessibility permission and it won't disturb Kaspersky AV main Accessibility permission. As for KSK, there's only one Accessibility permission as shown in my third screenshot. The main permission merged into one with the shortcut permission, so when I turned off the shortcut permission, it will also disabled KSK main Accessibility permission, unlike Kaspersky AV. The solution is for KSK engineers to separate the Accessibility permission like how Kaspersky AV did it.

I have the same issue on my Redmi Note 10. Hold press the icon didn't do anything. I can only move it around. Why would they added new weird feature when the old version works flawlessly... You can disable the overlay icon when you disabled KSK Accessibility permission. But disabling accessibility permission will also disable KSK ability to restrict websites.