Hi Andrey-,
Thanks for coming to Apple Support Communities for help today with Screen Time restrictions. It sounds like you are unable to remove some apps from Always Allowed in Screen Time.
In Settings > Screen Times > Always Allowed, the Phone app will always be available. That would be expected. The others should be removed if you tap the red "minus" sign., although removing Messages does come with a warning about Messages on other devices if you are using iCloud Messages. Check out: Use parental controls on your child's iPhone, iPad, and iPod touch,
If the apps continue to reappear after closing Settings and reopening, try restarting your iPhone: Restart your iPhone.
Also be sure your iPhone 6s is updated to iOS 13.3.1: Update your iPhone, iPad, or iPod touch
Let me know how it goes.
Have a fantastic day!