I just had this happen today, with a computer already running Bitdefender AV. I run Avast on another computer, but not this one.
I had only downloaded the update to CCleaner Free via the company website, which directed me to FileHippo for the installer. I submitted to VirusTotal to verify the file. Then I checked the advanced install option and everything looked good, so CCleaner updated to the latest version 5.40.
Then shortly afterward I noticed an Avast icon in my system start menu, and an Avast notification icon in my system tray. I really don't recall seeing any pre-checked Avast offers on the screen. So I uninstalled Avast after verifying that Windows Programs and Features showed the Avast install date as today. I double checked and do not have any Avast installers in my downloads folder, or anywhere else. I reran the same CCleaner installer again to see if there were any Avast offers available, and there were none. Mystery???
Anyway, Avast appears to be gone now. Do I really need to run avastclear? What remains behind if I don't do this safe mode step?