One suggestion that may help: If you have untested code such that you don't have sufficient time to refactor and retest it within the two week sprint, consider first making some other unrelated small change(s) to the code so that you can focus on writing tests for the first sprint or two. Perhaps you can identify several untested clients of the code you want to refactor; pick one client and make some other changes of some use to the business that will force you to write tests for that client. Once you're more familiar with the code, from working with it, and you have more tests, and you've possibly accomplished a few minor contributing refactorings, you will be in a much better position to accomplish the refactoring and the (now easier) testing both in one iteration.

Another approach is to make a copy of the offending code, refactor it, and then move clients one at a time to the new code. This work can be broken up across iterations.

And don't give up: Don't just accept that a large refactoring cannot be broken down into smaller steps. The easiest/fastest/best approach might take longer than an iteration. But that doesn't mean that there is no way to do iteration-sized chunks.