Blocking users from deleting history on Chrome/Edge via intune

AB21805 ,Chrome and Edge can both be managed using Settings catalog. I suppose you have a good reason to retain browser data and users are informed about it. (something about legal and privacy...)

That being said: 

• Create a device policy using settings catalog
• Search for "Enable deleting browser and download history"
• leave the switch at disabled

Note: You will have to do this for both the Edge and Chrome browser

However, have a look at the description:

"Setting the policy to Enabled or leaving it unset means browser history and download history can be deleted in Chrome, and users can't change this setting. Setting the policy to Disabled means browser history and download history can't be deleted. Even with this policy off, the browsing and download history are not guaranteed to be retained. Users may be able to edit or delete the history database files directly, and the browser itself may expire or archive any or all history items at any time."

You might wanna think about some other settings too:

• Delete old browser data
• Clear on exit
• etc.