I'll check once mine arrives in mempools to see how the fees compare. I tried a few different amounts (large and small) and the fee was different and always close to 0.1% (closer the lower you set the on-chain fee). You can select the sats/vbyte for the onchain fee and I could tell that a fee of 0 sats/vbyte still left the lower bound of a 0.1% difference unexplained for
Discussion
Hmm I’m guessing that it depends on how much data is being sent. Since it’s a multisig wallet, the data in the blockchain would be bigger.
Page 6 here cofirms they cahrge a flat 0.1% fee. Anything more than that appears to be the onchain fee to sent to your wallet
https://sideswap.io/resource/pdf/SideSwap_-_Peg_Service_-_Briefing_Book.pdf