Iterative, Evolutionary Refactoring is a good approach, but first...
Somethings that should not go unsaid...
To build on top of some high-level notes above, you should understand some important concepts from Complex Systems Theory. The key concepts to note circumvolve a system's environmental structure, how a systems grows, how it behaves, and how its components interact.
Sensitive Dependence Upon Initial Conditions (Chaos Theory):
A system's behavior will be amplified toward its most influential tendency -- meaning, if you've many Broken Windows which influence how a developer will write the next module or interact with an existing one, then this developer is more likely to break another window. Its even tempting to break a window just because its the only one not broken.
Entropy:
There are many, many definitions of entropy out there; one that I find becoming to Software Engineering is: The amount of energy in a system which cannot be used for additional work. This is why reusability is crucial. Entropy is found mostly in terms of duplicate logic and comprehensibility. Furthermore, this ties closely back to the Butterfly Effect (Sensitive Dependence Upon Initial Conditions) and Broken Windows -- the more duplicate logic, the more CopyPaste for additional implementations and it is more than 1X per implementation to maintain it all.
Variable Amplification and Dampening (Emergence Theory and Network Theory):
Breaking a bad design is a good implementation, though it seems all hell breaks loose when it happens the first few times. This is why it is sensible to have an Architecture which can support many adaptations. As your system heads toward entropy, you need a way for modules to interact with each other correctly -- this is where Interfaces come in. If each of your modules cannot interact unless they've agreed to a consistent contract. Without this, you'll see your system immediately start adapting to poor implementations -- and whichever wheel is the squeakiest will get the oil; the other modules will become a headache. So, not only do bad implementations cause more bad implementations, they also create undesirable behavior at the System's Scale -- causing your system, at large, to adapt to varying implementations and amplifying entropy at the highest scale. When this happens, all you can do is keep patching and hope that one change will not conflict with these adaptations -- causing emergent, unpredictable bugs.
The key to all this is to envelop your modules into their own, discrete subsystems, and provide a Defined Architecture which can allow them to communicate -- such as a Mediator. This brings a collection of (Decoupled) behavior into a Bottom-Up System which can then focus its complexity into a component designed exactly for it.
With this type of architectural approach, you shouldn't have significant pain on the 3rd term of "Red, Green, Refactor". The question is, how can your scrum master measure this in terms of benefit to the user & stakeholders?