The problem is more than double quotes, it also affects quotation marks on iOS. While out I wanted to look up something on our website and couldn’t find it.
I was looking for >> John’s << with a straight single quote in it. By default iOS changed it to John’s, which made me initially think there were no hits. It took a while to realise it was the same Smart Punctuation issue. This editor dialog is misdisplaying the single quotes!
Maybe not many people are searching using ASP on iOS devices. With Chrome or Safari on iOS, Google.com doesn’t get the same problem. Suggesting there is a way to turn of Smart Punctuation in the text input field.