There's something missing in this description of how the process works.
How does the restaurant know which credit cards are registered with rewards network and which are not?
There either has to be a system that reveals to the restaurant which credit cards are miles-earners, or the restaurant has to forward all its credit card transactions to rewards network for processing.
When I've inquired about missing dines, rewards network CS consistently refers to whether or not the transaction was "captured." Not sure what that means, but it sounds automagical.
Edited to add: In addition to the phone numner, there is a web form, linked from the list of one's rewards, for submitting missing dines. Also, there is a CS email:
[email protected]