Yes. I'd pay thousands for a pet dodo!
Maybe they could find something in their specific breed of not-actually-a-dodo that's patentable.
Or they could only distribute one sex of bird to the public, at least initially.
You definitely can't patent a corgi, but they're still quite expensive. Considering that dodo breeding is probably nontrivial, they could potentially make a profit. Depends on how the genetic engineering is funded, I suppose, and how well the work they do on the dodo applies to other animals. (If it's too dodo-specific it might not be worth it, but if work can be reused then it makes their next extinct pet even more profitable per unit)
Also, while it may be very expensive to clone a mammoth or a dodo today, you gotta figure that it will also contribute to figuring out how to do this sort of thing more cheaply at scale, which we might need considering the ongoing mass extinction of the Anthropocene.
//edit// But only after they become as ubiquitous as chickens or similar. I'm not a monster.