Worth contesting tow for tow earlier than noted?

I left my car out on the street while I was on vacation and got towed. I understand now I cannot park for more than 72 hours in the same spot and paid my ticket accordingly. However, when I picked up my car from the tow yard I saw an orange notice which said I would be towed if I did not move my car by 12/26 3:35PM, but my car was towed at 11:47AM on 12/26. This was a tow initiated by SPD. I tried to move my car right around 3:30 PM on 12/26 where I found it missing (I have a Lyft receipt time marked at 3:36 PM to the tow yard) and got my car out at 4:08 PM after waiting in line to get my car. Is it reasonable to contest this? The $300 tow charges hurts as a not a big earner.