A card not present transaction (CNP, TO/MO, Telephone Order / Mail Order) is a payment card transaction made where the card holder is not present physically with the card. CNP is well understood because it has always been associated with cards being used to pay online, where the possibility of fraud is higher, so the interchange rate has been higher to compensate for the higher risk.
Now with the mobile form factor, and with advancement in fraud detection technologies online, the online fraud might actually not be as likely as elsewhere, so there is pushback on the "CNP regime".
Also, mobile wallets that go "over the top" are generally stuck with having to pay CNP rates, just like PayPal because even though the card credentials are coming via the phone, they are not deemed to be "card present". This has been a point of contention as well as a concern of inhibiting innovation. The only exception has been hardware NFC secure element which has been classified as "card present", yet they come with higher fees because of inverse logic - because the fraud is lower, merchant should pay higher interchange!
The real source of abuse is when a payment credential is used without the owning customer's consent. Whether or not a "card" is "present" is becoming a moot point.
So the alternative to CNP should be Customer Now Authenticated (CNA). The whole industry needs to move to a system wherein NFC payments or other highly authenticated systems can be treated as Customer Now Authenticated so that a low transaction fee is charged.