Hi John M,
You can definitely delete invoices and an estimate in Method and Quickbooks and it will definitely make the proper changes in the other respective application.
For that specific invoice conflict, you can figure out why the conflict has occured by reading the message that appears below the Filter, Date Time, Type, Table, Record ID, User, Details, Delete from Method, Retry Sync to QB, Refetch from QB, Clear/Ignore column headings.
The first line of that message will give you a clear indication of why the conflict has occured. In addition to that, please click Here for the release notes for the improvements that we have made for the Resolve Conflicts feature of Method.
I hope that this helps.
Ronen