The main purpose of "Open Constituent" in the Raiser's Edge / Luminate Online (RELO) Plugin is for confirming if it's the correct record before making changes to it or linking it to another record. You can't actually edit the constituent record from within this Constituent Information area.

You instead have the option to unmark the checkbox next to an unwanted update within the initial Constituent Update screen of the plugin or to double-click on the incoming value and edit it.

If you wish to add information to the profile that isn't available in the initial update area (e.g. adding an additional phone number type) then you'd instead click "Process and Open", add the additional information to the record, and then click "Save and Close".