Don't bother with the app - check the data instead (if you need to)
Really, the only use case where you'd care about this kind of login is if the server has to trust the data produced by the app - and by extension, has to trust the app to be your app and not someone else's hack attempt. As has been demonstrated countless times, this is literally impossible. However you obfuscate it, someone will break it, given enough incentive (or just a lot of free time and boredom).
This isn't a new problem though. A perfect example of this kind of problem would be aim-bots in online gaming; or perhaps the regularly-reported data sent back to Pokemon Go about the number of steps you've taken. It's not possible to prevent people hacking these systems, because ultimately the data has to get back somehow, and there are incentives in gameplay for people who do. The solution taken by games designers is to check what comes back from the app and see whether it's valid. If moves are too straight and accurate to be human, it's probably an aim-bot. If your number of steps coming back to Pokemon Go is unachievable within that time at the maximum walking speed, it'll be rejected. Clearly this checking process can be complex, but this is one way you can solve it.
But then you also have to ask - does it really matter? My company makes industrial microscopy equipment. We simply don't care about secure connections between our controller boxes and apps on a controlling PC. Sure, a suitably dedicated person could spend some time and find the secret commands we use to calibrate the system. But the result then would be a system that no longer works properly, and we certainly wouldn't repair/recalibrate the system under warranty. There isn't a benefit to the user to do this, and it'd cost us time and money for something which isn't a benefit. So we don't bother.
Or quit now before the lawyers find you
If it does matter that this data is held securely - in particular, if it's about bank details, government files, or personal details under GDPR in Europe, COPPA in the US, or anything similar - then be afraid. Very afraid. The most likely potential consequence is "merely" your company being sued for every penny it has, so forget about that last cheque. That's the best outcome. If you play f***-around-and-find-out with bank details or government files though, that's serious jail time. And depending on where you're working, if you're the senior engineer then you may have to sign off personally on the work, which leaves you personally liable and not just the company.
If your management are suggesting this, your only option is to refuse. Your bosses can only give you instructions to carry out work that's legal, after all. If that doesn't cut it, leave now. (And if you're feeling so inclined, consider whistleblowing.)