There are more ethical issues about if you should dissuade than about how to do so, I think. But I'm only going to answer on how to ethically approach the latter, assuming your team can work out the former.
Banks (at least where I'm from) calculate interest amounts based on the lowest balance from a given period. So if I start with 1000, take out 100, add in 200, I'll get interest over 900. So from that perspective, you could argue that preventing (or at least postponing) my withdrawal I'm getting more interest. Showing people that withdrawal will cost them a small amount in interest can be that tiny nudge to stop them.
But, minimize the amount of popups/intrusions; always check if the withdrawal actually lowers the balance floor. If I start with '1000', add 200, then take out 100, I'm at 1100 which is above the floor of 1000. It's tempting to always show the popup, or to only compare versus the current balance (both easier to program and likely lead to less withdrawals), but that'd be unethical.
Another option is to ask them where the money should come from, to let users prioritize. This would be part of a much bigger framework. One of my current banks uses a 'jar' metaphor. It's a single account, but I can divvy up my money for different goals; new car, vacation, emergencies, and so on.
This has the primary benefit of making saving goals more concrete, so I'm more likely to add funds, but it also means I'm less likely to withdraw. If I want to withdraw money for a new couch... do I really want that more than a new car? Having a list of different budgets instead of a single aggregate number makes it easier to grasp your own finances, so that's a decent upside for the client.