A client is paying for a refactor but the manager says "we don't have time to write tests, the client is not paying for that" (when indeed they are in the end).
The client does not pay for refactorings or testing, and your manager shouldn't be made aware of it because it's part of your regular job. If they have so much insight in your day job that they start complaining, they're micro-managing and probably redundant (if they have the time / energy to look as closely at you / your team's work).
Looking at it from a manager's perspective, I think you'd want to do everything in your power to prevent such situations. Feels like there's a general lack of future perspective in many companies.