260nm depends on lots of other factors. Lets say it was 260nm, so 130nm radius. For the ship to see the lynx at this range, the lynx would need to be just over 10,000 ft up. I would guess he was at 50-2500 ft.
This is getting into the weeds now, but to be visible on the 1022 (or 996) radar at 48nm from mum (think this was the actual pigeons), the lynx would theoretically need to be at 1521 ft (ish). My guess is that the Mk8 would conduct surface search at above this, with the PIDD, so the ship probably did have the lynx on 996 and/or 1022.
But, then again, the ships radars detecting the lynx is very different from them being bothered about tracking it and certainly far removed from concerns about its fuel, pigeons or the fact that mum is probably running in the opposite direction (ship SOP).
Another Wild A&$e Guess !!