You can't. Not unless you can audit the app provider company.
Discussion
If you could audit, how would you tell? What would be the audit question that would decide it?
The provider would have to show you the actual dollars for all the supposed dollar positions. That would be easy with bank notes in a safe, with digital dollars it gets tricky. You would just get a level higher and needed to trust or audit the entity that provides this digital dollar position for your app provider.
How would you recognize that the digital dollar is a dollar.
Paper bills are a tiny fraction of dollars in existence.
To be 100% certain you would have to trace each digital dollar all the way back to the Fed.
FED does not know about most of dollars and most dollar loans are outside of FED jurisdiction.
I would assume that if a bank claims to have my deposit of say $100, it can prove that it has that money physically in a safe, or more likely a corresponding position in the forex market.
But I see your point. It's very hard to actually prove that your dollars in e.g. eToro or Revolut actually exist.
The question is, when could this become a risk? Maybe in case of a bank/app run? It probably devaluates the dollar too.
I am not even requiring any proof that they exist. I believe that the dollars only exist:
1.) in our heads
2.) in some position on the balance sheet of the bank
There is usually no “dollar position” - definitely not in a safe and usually not in a forex market (that would be expensive - swap either happens or not, that is not a position. a position would be future, but that has funding cost).
The balances that we see are actually same thing as DAI or LUSD, or Tether. I claim that there is no difference between these forms of dollars and most electronic dollars. Or no substantial difference. The only difference is payment network through which you can send it.
So, what do you think happens when I top up a Revolut account with 100 eur, exchange them for usd, over time the dollar goes up, I swap it back for say 110 eur and then take out my euros? Is Revolut voluntarily losing money?
No, they are not losing money. They might back it with an obligation with another foreign bank that made a usd-denominated loan.
When you change your eur for DAI, is MakerDAO voluntarily losing money? No, the exchange happened, but there is no US dollar. DAI was “printed” into existence by the form of a loan, backed by the obligation of the borrower to repay the loan plus interest to unlock their collateral.
At no point anywhere DAI touches the dollar system, except for the USD value of ETH given by price oracle.
In traditional banking system it is the same. It might be backed by loan obligation in a third party bank and it probably has absolutely nothing to do with FED or american banks. USD-denominated loans are how international trade works, 90% of USD-denominated loans are made this way (outside of the banking system).