I'll presume this is a manual trans. If not, then disregard the diagnostics below.
Unplug the reverse lamp switch (it'll be on top of the trans with two wires going to it). If the reverse lights go out, then the switch is probably shorted. (If they stay on, there's some other electrical issue that will probably require someone with electrical expertise to check.) To check further, remove the switch and check the bottom for damage. If it appears it has been struck or flattened by something, it's screwing too far into the transmission. If that's the case, replace it and be sure to get a new sealing washer (if applicable). If the switch looks okay, reinstall it into the electrical connector but not the transmission. Depressing and releasing the ball on the end of the switch should turn the lights on/off. If the lights went out when you unplugged the switch but this doesn't work, then you need a new switch.
As to whether this should be covered under warranty, I don't know the delivery date or mileage of the vehicle. In the U.S., the reverse lamp switch is covered for 5 years/60k miles for 1999 and newer vehicles. On older vehicles, the warranty will have already expired.