I don't really understand what they mean about hard code..
It means they haven't used the template override system.
Zen Cart is built to be able to "override" (not change or remove) the original code to make the visual and functional changes you want to the standard cart. This means that the original code is untouched and thereby easy (relatively) to upgrade.
Hard coded means they have hacked about with the original code making it a maintenance and upgrade nightmare....it needs to be re-done the correct way before upgrading or making further changes.
Probably/definitely better from a project planning/costing point to view would be to start with a clean 1.51 cart and correctly implement the visual and functional changes required to mimic the existing cart and add your new requirements. Otherwise, fixing your existing cart may be "how long is a piece of string"/Pandoras box for any developer.