Is it unvented ? If so, it is already 99%+ efficient*. If it is a vented factory fireplace, try to look up similar models and find their efficiency ratings, they are probably still efficient enough to be worthwhile. Units with fans can improve efficiency as well. If they are just gas logs thrown in an existing woodburning fireplace turning them on could actually be worse than leaving them off. Replacing them with a more efficient unit would probably not be worthwhile unless you plan on renting for a very long time.
*There is a lot of debate around non-vented gas heaters as the combustion products end up in the living space. In theory, the only combustion products should be H20 (which can cause moisture problems) and CO2. In reality, natural gas has traces of other compounds that end up in the air as well, some people claim to be sensitive to these compounds. Unvented models should be equipped with a low O2 sensor that turns them off if they start to deplete the oxygen (which would eventually sufficate you). There is also a higher possibility of the production and build up of CO in a malfunctioning unit which is fatally poisonous in many cases, unlikely though, if all the proper safeties are in place. Many codes now prohibit un-vented gas logs/heaters for these reasons, but many people still use them without any issues. If you have one and decide to use it, at least make sure you have a working CO alarm, watch for moisture problems, and do not run it while sleeping.