This seems like silly thinking. I don't think anyone would reasonably believe they put all the money they receive into powder packets. Every $1 you give them will immediately save 14 lives!
They're just saying that's one thing they do with the money, a part of their budget. You should be more concerned with what a given charity's administrative overhead is. How much of that $1 goes towards the $0.07 packets, and how much pays the administrators.
If charity1 has a 20% overhead and then spends the rest on saving the life of a child for every 1000$, while charity2 has a 40% overhead but saves a child for every remaining 500$ spent, which one is better? Overhead is just one factor of a charity's efficiency.
Of course in this case the cost of the powder is just a small factor, and you also need to consider the cost of distribution and other overheads. And the fact that the effectiveness probably drops off at some point. Obviously just spending 1B$ is not going to save 20 billion children, there aren't that many children that need these ORS packets.
If they already have so much money that they buy $0.07 packets for everybody that needs them, then your additional donation won't pay for any additional packets, and you can leave it out of your analysis. Donating won't affect the packets.
But if they don't have enough money to vaccinate everyone, and they're putting as much money into that as they can, then the effect of donating $50 is that three more children are vaccinated.
On the third hand, if they already have enough funding for everything they want to do then your donation is not useful, even if they have low administrative overhead. It won't lead to any extra packets or vaccinations compared to if you didn't donate.
Administrative overhead is good to take into account - if it's very high then something fishy could be going on - but the main thing is the effect of your donation.