Viret - If you delete the records using the API, then the records should be removed from the conflicts area.
Unfortuantely, the Conflicts listing is not an exposed table (in Method or the API).
You mentioned in another post that the conflicts were "DeleteFromDesktop", but that the records were actually not even in the database anymore. Two comments on that:
1. If they are marked for deletion, but still exist, then you can't see them except through the conflicts area.
2. However, if they are truly gone, you have a quick solution available to you: (a) in the Resolved Conflicts screen, click Clear All. This will make them go away from conflicts, and make them visible in Method again. Then (b) do a Full Sync. If the Full Sync finds that they have been deleted from QuickBooks, then it will put them back into the Resolved Conflicts screen. If it does not find them....well....your problems are solved!
Also, if you use the API to delete all records in a table, the valid ones WILL get deleted from QuickBooks. You don't want that. Before you go that route, let's see how far you get with my suggestion above.
The big question really is, how did this happen in the first place. Did you sync different database files with this account?