It's too late to gain trust from people. The delete Coinbase movement has already started and I think it will go quite long. It's interesting if they admit their due diligence is lacking while people who spent just 10 minutes browsing can know why Neutrino is shady, or at least have a lack of ethical ground. I believe sooner or later this issue will be forgotten, but Coinbase for sure won't gain trust from major users.
The #DeleteCoinbase movement is only going to hurt Coinbase if there surfaces a worthy competitor that is on the same level as Coinbase right now. This implies, as figmentofmyass correctly pointed out, low deposit fees, a clean UI and smooth UX. As of right now, there's no such competitor on the market right now and Coinbase knows that. Binance's attempt has not really been gaining traction, struggling to get a single bitcoin of trading volume on their main pairs. Binance is simply to expensive to use right now. I hope Binance Jersey is some sort of prototype for a final version on their main exchange.