When attempting to remove and exchange account from an iOS device, the remove button is grayed out or is not visible.
Reboot the device and attempt removal again.
If removal is still not possible, check with user to see if a mobile device management app has been installed on the device. If the app is still installed, the user will need to remove it in order to continue.
If the app has been removed and the delete or remove account option is still not available, go to Settings > General > Profiles on the device and delete the old exchange profile. In some cases, multiple profiles may be listed for the account in question. Each profile may need to be removed individually, but it may only be possible to remove one - which, in turn, should remove the rest. After removing the profile(s), the user should be able to remove the old account. It is highly recommended that a full backup be completed using iTunes before attempting removal of a profile.
For more context, refer to the Apple Support discussion in the article listed below: