while peTbl.Locate('peID',peID,[]) do  
    peTbl.Delete;
end;

Here is a test app:

In Button1Click (below)
                  
If you run the program with one person in the database, then
LocateBeforeDelete = True and LocateAfterDelete = true;

If you immediately click Button1 a second time, you get a True, followed by
an Exception on Delete.

If you Close and then Open the table after the first locate, things work as
they should.

procedure TForm1.Button1Click(Sender: TObject);
var
  LocateBeforeDelete, LocateAfterDelete: boolean;
begin
  {--- locate single record before delete (Returns True)---}
  LocateBeforeDelete := EDBTable1.Locate('peID', 1, []);
  if LocateBeforeDelete then
    ShowMessage('Locate Before Delete = True')
  else
    ShowMessage('Locate Before Delete = False');

  {--- delete single record in table ---}
  EDBTable1.Delete;

  {--- locate single record after delete (Returns True)---}
  LocateAfterDelete := EDBTable1.Locate('peID', 1, []);
  if LocateAfterDelete then
    ShowMessage('Locate After Delete = True')
  else
    ShowMessage('Locate After Delete = False');
end; {Button1Click }