What we have learned
ToastTab seems to offer the functionality for a restaurant to offer gift cards directly on their site. They pass through 100% to the restaurant without any charge according to a text chat we had with them 3/19
Square may charge a fee but seem to offer easy technology for a company to add gift card options to their website. We have seen companies like this waive fees and hopefully Square will so the same.
Some folks use 'Giftly' and Shopify to set up the gift card option for their business. We don't know much about these services but merchants may want to check these out as an option.