Yes. The app makes it much more difficult for women to subvert the oppression. Before the app the government used little paper slips to grant travel permission, now the "guardians" get SMS notifications when a woman's passport is scanned.
I’m not advocating that anybody DDOS their SMS system with fake alerts. But at least an app protects against that to a greater degree than an SMS solution. The app creates a safe space for oppression.
The app is not the technology that makes this possible. It's just a webview around their website, and the SMS messages (not push notification) are sent directly to the phone via the cellular network.
Will anyone be able to silently leave the country if this app was pulled from the store? No, the SMS messages would still be sent, because they have nothing to do with the app.
On one hand I think Apple and Google should drop this, and never should have hosted it. On the other hand I disagree with your assesment that “every little bit helps.” Too often these largely symbolic acts do little more than assuage guilt, they don’t improve anyone’s life. Think of it this way, if you’re riddled with cancer, and I offer you a single dose of chemo, you might reasonably complain that I’ve done nothing for you. If I then shrugged and said that at least I tried, and every little bit helps, you’d be well within your rights to laugh in my face.
Sometimes helping just a very little bit is as good as doing nothing, or even worse, because doing nothing at least is unequivocal in terms of moral culpability. In this case we’re talking about Saudi Arabia, a country with vast riches because we all buy their oil and kiss their asses. It’s like my government (U.K.) crying about Yemen while selling the Saudis more weapons.
Helping is a good idea, we shouldn’t host these apps, shouldn’t sell them weapons, and frankly shouldn’t dare to pat ourselves even slightly on the back for it.