Try to see the file attribute of the .DBF Table if it mark as Read Only. Or Do you have full rights on the .DBF file?
or you can try these one...
Dim objCon As ADODC.Connection
Dim ConStr As String
Dim SQL as String
ConStr = <Place your connection string here>
objCon.Open ConStr
SQL = "DELETE FROM <tablename> WHERE <condition>"
objCon.Execute(SQL)
objCon.Close
Set objCon = Nothing