Sent ETH from an old Binance account to Robinhood on the wrong network? Is it really lost??

Hello! Last night I went through the process of digging up my old Binance account from 2017 to see if my crypto had gone up recently and I had about $1600! I was excited, but wanted it out of there and into one single platform (also, it was NOT Binance US, so I couldn't do anything but withdraw). I was happy to find it easy and I transferred my Ripple to Robinhood no problem. The Network option said "Automatically match the Network" and everything went through quickly. That was worth $600. Then I tried my $1k worth of ETH and the Network option didn't say "Automatically match" and I had to choose 1 of 4 options. With no explanation of the differences, I looked at the transaction prices and transfer times and chose the cheapest fee, Arbitrum. Nothing on Robinhood or Binance gave me warning that I need to pick the CORRECT network. I only found out after digging deeper on Robinhood to find that it doesn't accept transfers from other networks. Everything from customer service on both ends says it's lost forever. And googling also tells me so. Any help here would be appreciated. And if it's lost forever, I want to know for sure before I give up. Thanks