I was thinking about a way of running a monero payment gateway node for quickly identifying incoming transactions.
For the mobile phone, after making the payment, instead of outsourcing the task to remote node, you could also send them Transaction ID, which they can quickly find in mempool (if they accept 0-conf transaction) & verify it.
Or, If the transaction is confirmed, you could send them confirmed Block ID, which they can download from a remote server and find the transaction (with transaction id) and verify it.
Instead of maintaining a remote node, this can be done in any mobile-phone, they can purge the data if the required transaction isn't found, or this can be done on any server without running any node.
they can have some remote peers to download specific block to verify the transactions.
some sort of things like that, just came into my mind.