You really do not have to much of anything really. The machine they use to bury the cable does not do a lot of damage. It will look a bit like mole tunnel of just a line of fresh dirt in a straight line. Come spring once the grass starts to grow again will be gone in no time at all. If anything just go out and step on the line of dirt it mounds up to level it off.

As for winter watering not much to do there either. IF it gets really dry water once a month or so. Or if you hear a really cold snap, and I mean cold like low twenties or lower, you can water to add some freeze protection. If you have mowed properly at a height of 3 inched or higher freeze damage should not be a problem your location.

All the dirt that comes out of their trench MUST go back. Don't let them take any away or sweep it away from the scar they leave. Mound it up and let it settle back into the trench. It might take 3 years to return to flat but if you remove any of it, it will become a depression.

Water every four weeks in the winter. I guess I should ask where you live before answering that. Your zone is sort of meaningless to grass issues. We need your town. The suggestion for once a month would be for more toward the coast. If you live more toward the Mexican border, then you are in a desert and may need to water every 3 weeks because of the soil and low humidity conditions. If you water weekly you might keep the grass green all winter. I just bought a home in George West, TX and am learning about gardening in a more desert-like climate.

If you can do so, watch them do the job. If they do not tamp down the sliced ground near the end of the project, suggest you water the line then walk it to help "seal" it.