I'd say it depends. If you do it right, you'd change the 8ga to 6ga for the entire run. 6ga wire isn't expensive for those lengths.
That said, the other factor is the potential power draw from your new tub. If it draws anything over 40A with everything running, then I'd suggest upsizing the wires. If it'll never draw over 40A, then you can get by with your existing wire.
Our tub will never draw over 40A, but the manual said to use #6. If #8 is used, and there's a problem, the warranty will be void. This particular tub has other options that would push the amp draw over 40A, which is why it's worded as such.
The wire run from our GFI to the tub is 20', even though the GFI is only about 7 feet away. Per code, the GFI must be at least 5' away from the tub... so how could you have a 5' run of 8Ga wire from your GFI to the tub's junction box?