By default, the One-click Completion feature does not require any information to be entered for a Call Objective when the user records a Call. However, additional Call Objective fields are still displayed on the Call page layout Online.
Only Read Field Level Security (FLS) is provided for the One_Click_Completion_vod field on the Call Objective object.
Once Edit FLS is granted as well, the expected behavior occurs. This means that the extra fields are not displayed on either of the platforms.
CRM Help Documentation: Call Objective Types