Do I have to just edit it so the initial one will be replaced?
Essentially, yes. You can’t delete your own discussions on the forum. However, if you replace the content with “delete please” a moderator will usually see it and delete it for you. Just try not to do this too often since a single moderator has to handle it for you and there are only a few!
There is no option for deleting any conversation on Fiverr. Only customer support have right to do this. You can request to customer support.