Honestly they could do away with the mechanic. It's no wonder that new high-end hypercars introduced in updates, such as (in order): the Porsche 918 Spyder, Bugatti Chiron and Aston Martin Valkyrie, don't need any invitations at all.
Or if anything, the invitations can be permanent, but you must meet certain requirements before you can attain them, such as:
Aston Martin - Have at least Cr. 5,000,000 worth of garage assets from Aston Martin.
Bugatti - Reach 400km/h on at least ten cars.
Citroen - Win 10 races each with the GT by Citroen Race Car (Gr. 3) and GT by Citroen Gr. 4, a total of 20 races.
Ferrari - Have at least Cr. 20,000,000 worth of garage assets from Ferrari.
Lamborghini - Own at least one car from the Countach, Diablo, Murcielago and Aventador model families.
Pagani - Win 10 races with the Zonda R.
Porsche - Own at least one model from every Porsche 911 generation (901, 930, 964, 993, 996, 997, 991 and 992).