Thanks to the magic of physics and math, you can calculate a lot of that into software, and adjust on-the-fly.
My guess is that they'd be allowed/made to relearn some of the behaviour they already learnt for 1g conditions. Without having poked at BD's press releases at all, I've a feeling that a lot of the 'stagger recover' from both deliberate pushing and awkward terrain conditions was 'learnt', not painstakingly programmed in, except for maybe some initial guidance as to how to narrow down the behavioural search-space towards an anthropocentric expectation. The 'press-up' recovery from having fallen flat on its face, if tried in lower-g, would potentially send it crashing over onto its back, until it learns to push slightly lighter/slower for Mars-gravity.
Plus, I'm guessing they can do simulated 0.38G testing in water chambers and Vomit Comets.
Proof of concept that they are versatile, but water-testing would involve an artificially over-thick 'atmosphere', and an actual learning algorithm might end up going for windmilling arms 'swimming' its way back upright, in a way that would not work in Mars's air... And if Earth-air thickness is at all exploited right now then that ununtentional reliance will have to be unlearnt too.
(And can they, or rather
do they, use the VC in a flight plan that produces low-g that's still not actually (effectively) zero? As in, doubtless they can (just don't go with quite as extreme a curved flight), but how easy is it to maintain fractional-g without wobble, if they're mostly configured/pilot-trained to aim for zero?)
My thoughts are that a decent versatile robot to send as constructor would have a stable rover wheelbase (active suspension giving hexapodal-walking capability, built in for wheel-unfriendly situations) with torso/head/arms atop/in front for 'fine work' (autonomously or with remote telepresence by a human operator sat in a rig) and a crane-arm-cum-extendable-multiheaded-tool thing on the back (with carrying space between for building components/materials). Add a retracting dozer-blade/stabilisation pad, and it could deal with
many situations, even toppling over.. As long as it doesn't lose its ability to think and/or communicate.
(Counting up, there's
at least 40 degrees of freedom, even ignoring end-effector/tool control, which is a lot of opportunities to go wrong, with a large number of non-interchangable components, but if it damages a wheel-motor it could limp back to base on five, four, even three remaining wheels or even
actually limp home in slow-walk mode, or else buggyboy2 goes out to meet it with a spare part and effects a field-repair or helps tow it back.)