The American team has made big revisions to the sidepod, engine cover bodywork and floor of the VF-23 ahead of the final five races of the current campaign, in the process becoming the final F1 squad to switch to Red Bull's downwash sidepod design path.
But with little time between the Qatar and United States Grand Prix flyaway rounds and with lengthy customs checks in the former to consider, the team opted not to assemble the new parts on its cars at its Banbury base.
Speaking in the Austin paddock on Thursday, Steiner outlined how "the cars came here [and] we rented a workshop outside here".
He added: "We got the cars on Sunday [a week after the Qatar race and five days before practice at the Circuit of the Americas], we took the cars to a workshop and the new parts were flown in from Europe and we fitted them and we brought the cars into the paddock here on Tuesday."
When asked if anything on the VF-23 had changed other than to the upper and lower aerodynamic surfaces, Steiner said: "The radiator ducts a little bit, which you cannot see.
"Otherwise, we left the radiators in the same place because to change these things so late is also not possible.
"Because the main thing is the side impact structures – you would need to homologate a new chassis and that is just too much at this stage.
"You couldn't even do it. You could maybe get it done for the last race, but that doesn't make sense.
"But, in general, we didn't have to change anything else. We changed the floor obviously, as you can see, and all that stuff.
"But under the skin almost nothing was changed like radiators [and] all the electronics boxes stayed in the same place as well."
Haas's drivers Kevin Magnussen and Nico Hulkenberg hope the changes can help the team solve the major in-race tyre wear issue that has hampered it this season due to an aerodynamic imbalance that is additionally exposed in windy conditions.
Magnussen said it was therefore, "nice to see the upgrade on the car, finally".
"We haven't had many upgrades to the car this year," he continued. "It's been a tough year in terms of finding performance.
"The guys have been really struggling this year to make gains on the car we've had. And I think this upgrade is an exciting one, because it's very different.
"On paper, it's not actually meant to be more downforce as such, but it's a new concept. And it's hopefully the concept that we'll be using for next year's car.
"If it's not a big gain in performance, then at least it's some good learning and research into next year. A big problem with our car this year has been that it doesn't treat the tyres very well in the race.
"The pace that other people are able to maintain, we seem to fall off much more and that problem might be – although you're not putting extra downforce, like, peak downforce – if you can better the characteristics of the car, the through-corner balance and, hopefully, the structure and the strength of the flow on the car, that could solve that issue or help that issue.
"So that's, of course, what we're hoping for. Nonetheless, it's exciting."