It always depends on the circumstances. If people don't like the term rewrite, you can just call it re-factoring or adding unit testing. You are probably using something from the old codebase, right. If anyone asks why something that used to work is no longer there, you can explain that you found bugs, and so you temporarily took it out to add more testing.

Although, rewriting can be a lot of work. While there may be a temptation to rewrite everything overnight, it can be quite difficult to pull off. Although, I think devoting some time to a rewrite attempt may help you gauge the total time it will actually take. If it proves easy enough, you can go for it.