If you double-click a cell or press ENTER to start editing, the whole cell text is selected automatically. FYI: if you press an alpha-numeric key to start editing, the cell text is replaced with it or the pressed char is appended to the cell text depending on the value of the KeyPressBehaviour property, and the caret is placed automatically at the end of the edited text.
Most likely, you use the RequestEditCurCell method without specifying its only parameter to start editing, which is equivalent to double-click or ENTER. However, you can adjust the selection (caret position) after the editing has been started but before the user is able to enter new text in the TextEditStarted event. For instance, to place the caret at the end of the edited text, use event handler like this:
Private Sub grdCust_TextEditStarted()
grdCust.TextEditSelStart = Len(grdCust.TextEditText)
End Sub
Ideally if one clicked on the cell with the mouse the cursor would be placed at that point but that is probably asking too much.
Theoretically this can be also done using the described approach, but the main problem is how to determine the caret position in the text clicked in in the cell. Sure, this can be solved using a lot of API calls, but obviously, this is too much for this task.