IMO, as the off-street order is only amended by these revisions and not revoked and remade then you need to see the whole order to see whether there was and still is an existing provision regarding how free periods are obtained.
This needs more digging into than I can do right now, but I think you might be in the clear (although you'll likely have to go all the way to the adjudicators to win).
Knowing Barking & Dagenham's slapdash approach to following the proper processes and procedures, I had a quick look at "THE LONDON BOROUGH OF BARKING AND DAGENHAM (OFF-STREET PARKING PLACES) AMENDMENT No. * ORDER 202*", which I think is the most recent off-street parking order, and it looks to me as it they have cocked up the paperwork. If I'm reading this right, the order does include a requirement to book by phone for free parking in note (1), but only for schedule 2 on-street parking, not off street parking in car parks.
Can someone else take a look at https://www.lbbd.gov.uk/sites/default/files/2023-11/ID373%20%20PBP%20%20Tariff%20amendments%20NOI.pdf and check I'm reading it right?
Frankly, I don't think you are on solid grounds at all, to take this all the way to London Tribunals, which is what is implied if you wait for the Notice to Owner. This is because whilst you say " Unfortunately, I did not notice the small writing underneath that required 'all free sessions need to be registered with the app'", it is difficult to see how you might have missed it, as it is very clear what you have to do, and is directly below the 2 hour free limit statement.
I say London Tribunals because the council will refuse your reps to a Notice to Owner and may not re-offer the discount. Certainly if they don't, it is a no-brainer to go to London Tribunals, but with what argument ? So you'd be risking the full PCN penalty on a weak case. Not good.
Of course, somebody may come up with a "technical" appeal argument that could win for you, so wait a bit, but don't miss the deadline for payment of the discount if that is to be your decision.