had taken their products off sale when it launched its own similar tools.
But Apple said the apps were removed because they "put users' privacy and security at risk".
It said the apps had been given time to make changes to meet Apple's rules.
The latest version of Apple's iOS mobile operating system added Screen Time tools, which let people see how much time they spend using their favourite apps.
The tools also let parents control how much time their children can spend on apps and websites.
Some app-makers claimed Apple had removed their products from the App Store after Screen Time was launched, and said it was trying to limit competition.
However, in a blog post, Apple said it had taken action against apps that were using "risky" Mobile Device Management (MDM) to control children's smartphones.
Many corporations and organisations use MDM to control what employees do on their phones. It lets businesses keep an eye on what staff are doing, and even wipe their phones remotely.
Apple said it was not appropriate for family-focused time management tools to use MDM.
"MDM gives a third party control and access over a device and its most sensitive information, including user location, app use, email accounts, camera permissions, and browsing history," Apple said in a blog.
"It is incredibly risky - and a clear violation of App Store policies - for a private, consumer-focused app business to install MDM control over a customer's device.
"Contrary to what The New York Times reported over the weekend, this isn't a matter of competition. It's a matter of security."
The company said it had given a number of affected apps 30 days to submit updated software that did not break its rules. It said many of the companies did make changes and were not removed.