Exactly. Returning from orbit is "easy", you just go into a free-return trajectory and don't even do much of a burn at Mars, if any at all.

Getting a sample from the surface basically means you need to do a deceleration burn to get into orbit, and then the reverse after grabbing the sample (which itself must be accelerated to orbital speed). No small thing.

A free-return trajectory doesn't enter orbit around a body, indeed its appeal is that if your propulsion fails while on such a course, you'll coast home "for free" rather than enter orbit around your target or drift into deep space.

Entering orbit almost always requires an orbital insertion burn, and in the case of an Earth-Mars Hohmann transfer definitely does.

Your point stands though: returning from a fly-by (including a free-return) requires much less fuel than returning from orbit, and even that's much easier than returning from the surface.

For fun, take a look at rotovators (AKA "momentum exchange tethers") that could make orbital capture/departure—and even landing/launch—"free" on bodies with minimal atmosphere.

Correct, I misspoke: My first use of "orbit", I should have said "the area up around the planet, not down on the surface.

The difference in difficulty (mainly, fuel requirements) between a flyby and an orbit is a crucial distinction often overlooked.

SpaceX isn’t planning to enter orbit around Mars but instead do direct entry.

How do you retrieve a surface sample on a direct-entry mission?

You land on Mars. Refuel. And launch again direct to Earth.

A SpaceX vehicle returning from the surface of Mars.

You're saying the vehicle will bring all the fuel needed for a return flight to Earth down to the surface of Mars and then back up again? Do you have a link with a description of how they're going to do this?

No. It will make the fuel from Martian resources like water ice and the CO2 atmosphere. Using solar power. First to split the water to oxygen and hydrogen using electrolysis, then use the hydrogen with CO2 to make methane (& some water which is cycled back to the electrolysis step) using the Sabatier reaction. This is done on the International space Station today, by the way. The methane on ISS is simply vented (as the point on ISS is to recover the oxygen from the CO2, which is most of CO2’s mass). It takes a lot of energy, so there will need to be very large solar arrays on Mars, but it’s possible.

This page describes the process: https://medium.com/spaceinmylifetime/how-spacex-will-refuel-...

Call me overly cynical, but I don't see Musk getting this done in time to be back in 2031 and win the race.

Well, he’s competing against a gov entity, so his schedule slips are going to be much less than theirs.