The Martian Sol is 24 hours and 37 minutes long, so daytime at a fixed point on the planet's surface will drift in and out of sync with a fixed point on Earth's surface, and keeping the tradition of a 7-day week would have similar implications. Roughly every 39 days on Mars, 40 days will have passed on Earth.
Suppose the Martian colonists want to set up their weekly calendar so that their weekends occur roughly at the same time as they do on Earth. Maybe they want to not be bothered on weekends. Maybe there's some other social or religious benefit. The exact reason why is not important here. Also assume this is sometime after basic terraforming so that people live above ground.
They certainly could go by Earth time and avoid the problem entirely, but this quickly and regularly gets them out of sync with the natural biological instinct to go by whatever the sun says. Living your daily life in darkness for 19.5 days on, 19.5 days off doesn't make a lot of sense.
You could do something like leap days to handle this, but those 37 extra minutes do not divide evenly. It's almost a 6 week cycle, so doing something like skipping Wednesday every 5th week will cause Mars weeks to drift ahead slowly. Therefore you would need to create an additional rule of some regular interval of not skipping Wednesday on a fifth week. But then that creates another syncing issue. Layers have to be added until enough precision is achieved, just as we do for leap years.
Are there other alternatives that are mathematically consistent without being too difficult to remember? It would be pretty awful to go to work on a Saturday because you forgot that Friday got skipped this week. Or you could miss work because you thought Friday got skipped, but it wasn't.
If skip days are the only reasonable way of handling this, is there a strategy that could be used to help people remember without it feeling like which day is skipped is arbitrary and unpredictable?