I assume all of your personal data and installed programs are on the same partition as Windows?
As you imply, if you restore your own Macrium image, it would overwrite the fresh Windows installation done by HP--and I assume you do not want to do that.
In such a case, I think you would be forced to reinstall all of your own programs individually after HP returns the machine. You can't selectively retrieve installed programs from an image without an outright restoration of the image--which you don't want to do.
You could restore your personal data files from the Macrium image, but I wouldn't rely on that. Instead, I would do a file by file backup of personal data to an external drive of some type before HP touched the computer. You could use an application dedicated to that type of job or just do a drag and drop with the mouse.