I have CCleanerPro 5.28.6005 which was not able to delete+uninstall latest MBAM 3.0.6.1469.
After removing its home-directory by hand there were found many registry problems like the following:
ActiveX/COM Issue LocalServer32 C:programs\Malwarebytes\Anti-Malware\mbamservice.exe
but CCleaner did not fix MBAM registry too They appeared again after analyzing!
Use the MB-CLEAN tool to uninstall MBAM and get rid of remnants.
See thread here
https://forum.piriform.com/index.php?showtopic=48011&do=findComment&comment=281774
Download available in 2nd post of the thread.
OK. I will try MB-clean but what's the problem in CCleaner to do it?
N.B. the latest MB-clean link:
https://downloads.malwarebytes.com/file/mb_clean
MBAM is having 'a few issues' with their new version 3 which I'm sure you'll know about if you read their forums .
(I altered your direct download link and put it in a code box so folk can just copy and paste the url if they want it, as it can be easy to accidentally click on a direct download link)
Let us know how you go on.