As your form already contains code to add a row, then delete all the rows except the first to begin with and only add the rows as you require them, however to address your question the following will delete the row the cursor is in.
Code:
Sub DeleteTableRow()
Dim oCC As ContentControl
If Selection.Information(wdWithInTable) = True Then
For Each oCC In Selection.Rows(1).Range.ContentControls
oCC.LockContentControl = False
oCC.Delete
Next oCC
Selection.Rows(1).Delete
Else
MsgBox "Selection is not in a table!"
End If
End Sub