Yes, action with domain admin accounts must be risk-managed.
That field is normally fairly static information for humans. It sounds like you are harvesting manually updated data from Moodle and putting it into AD. Is it acceptable to update that field daily, instead of instantly? Can the company supply a daily text file of changed ID data? Would you be prepared to schedule a PowerShell script nightly to insert that into your AD? Would you be any more reliable/trustworthy than the Company?