Q: How can I opt-out notifications from eBay download center or File Exchange?
A: Unfortunately, you can't opt-out of email confirmations from eBay. Just as if you went to eBay file exchange yourself and were trying to upload a file, eBay requires an email address to submit and there is no way to opt-out of the email confirmation. See file exchange page for uploads -->> https://bulksell.ebay.com/ws/eBayISAPI.dll?FileExchangeUploadForm&ssPageName=STRK:ME:LNLK
So everytime the file exchange receives an upload or download request to synchronize your active items and sold items, you will receive an email confirmation and there is no way around that. It's just the nature of file exchange.
I suggest creating a filter in your email account to automatically either label those emails or send them to trash if you'd prefer.
The only way to stop them from this side would be to uncheck the options in your chrome extension -- however, that would in turn make the extension stop sending and receiving files on your behalf and your items won't be updated.