Yes, you are being picky, especially as a "final" rejoinder to a pilot politely and modestly saying thanks to ATC on the occasion of his retirement!
Speaking as another pilot from Thud's "All Jet" era at RAF BFTS (I too carried out my RAF basic flying training, straight from civvie street onto the JP) "Finals" is just a throwback to the correct military call, as in "Finals, three greens". I do now say "Final" and don't bother saying the "Gear Down" part, but it is easy to fall back on what we were used to saying for twenty odd years.