How can I flip selected text horizontally without leaving the original text behind in Photoshop?

I have a CCTV image with horizontally mirrored OSD text (date/time and camera number).
The photographic scene has already been corrected with Horizontal Flip, so I do not want to flip the entire image again.
I want to correct only the OSD text.
I can successfully select the OSD text using a rectangular marquee combined with Color Range. The text selection itself seems accurate.
However, when I use Edit > Transform > Flip Horizontal on the selection, the original text appears to remain underneath the flipped text, so the two versions overlap.
I also hid the other layers, but the overlapping text was still visible.
What is the correct Photoshop workflow to replace the original selected text with its horizontally flipped version, without affecting the surrounding background?
Would using Transform Selection, Channels, or another method be more appropriate?