Controlled Folder Access is not about 'memory' or system files.
It is about protecting your own files from ransomware.
It is found in Windows Security, Virus and Threat protection, Ransomware protection.
It provides an additional layer of protection when programs try to make changes to files in your personal data folders, like your Documents, Pictures, and Desktop folders.
The only thing that I am aware of that CCleaner would put in any of those folders is a registry backup if you tell the Registry Cleaner to make one.
Obviously that would not be happening if you didn't have CCleaner open and run the registry cleaner.
Why CFA is being triggered at startup by CCleaner (or what it thinks is CCleaner) I have no idea, but CFA does get things wrong and can be overzealous.
(Microsoft admit so themselves).
I think that the first thing I would do is a Restart (not a shutdown) of your computer and see if that stops the notifications.
Sometimes things Windows can get 'stuck' and carried across Shutdown/Boot - A Restart can clear these.
If that still doesn't work then I'd uninstall CCleaner, Restart, and reinstall CCleaner.
And as a precaution you may want to run a virus/malware scan on your computer just to make sure that it isn't something else pretending to be CCleaner, although that's unlikely some malwares do like to pretend that they are well known apps.
For info what is your Windows version/build?
I assume that your CCleaner is installed at the Standard Location- "C:\Program Files\CCleaner\....".