DrawText is more like a spray can - it paints over top whatever is already there. I'd recommend switching to SetWindowText. The difference is DrawText is more like a canvas rendering call, and doesn't consider much about the type of control it's drawing to. SetWindowText is an explicit "set the text of this window to this specific value", and is specific to text-based controls. More to the point, it will replace the current text with the new text value.
If you absolutely must do it with DrawText (i.e. you prefer a canvas approach as above), then you'll have to manually clear the text area yourself with something like InvalidateRect() (using the RECT of the text area). Or, by drawing a rectangle equal in size to the text area and with the same color as the background. Let me know if that's not enough detail.