How to disable Google asking permission to regularly check installed apps on my phone?

On Android prior to 4.2, go to Google Settings, tap Verify apps and uncheck the option Verify apps.

On Android 4.2+, uncheck the option Settings > Security > Verify apps and/or Settings > Developer options > Verify apps over USB.

If you want to turn off app verification programmatically, you can do so with the following code:

boolean success = true;boolean enabled = Settings.Secure.getInt(context.getContentResolver(), "package_verifier_enable", 1) == 1;if (enabled) {    success = Settings.Secure.putString(context.getContentResolver(), "package_verifier_enable", "0");}

You will also need the following system permissions:

<uses-permission android:name="android.permission.WRITE_SETTINGS" /><uses-permission android:name="android.permission.WRITE_SECURE_SETTINGS" />

Also worth noting is that the "package_verifier_enable" string comes from the Settings.Glabal.PACKAGE_VERIFIER_ENABLE member which seems to be inaccessible.

It is also available in general settings

Settings -> Security -> Verify Apps

Just un-check it.

( I am running 4.2.2 but most probably it should be available in 4.0 and higher. Cant say about previous versions ... )