Hello!
I added this code to your mod and the inscription no longer appears:

script.on_event(defines.events.on_rocket_launched, function(event)
local rocket = event.rocket
if rocket.get_item_count("satellite") > 0 then
game.set_game_state{game_finished = false, player_won = false, can_continue = true}
global.send_satellite_round = false

else
game.print({"no-satellite"})
end
end)

Would you then see teh statistics like with a normal "game-over" message or not? And even if this windows occours, shouldn't you be able to continue playing until you have enough from this game?

Thanks. I'll test it out and see if that resolves it.