It seems that after a Trello update yesterday, when you specify a URL in a checklist item and then add some markdown to its name, it breaks the link's image.
For example, if you want to add an item to a checklist with Google's link, simply writing Google between "[ ]" followed by "( )" with it's URL it works fine.
However, if you want Google to be displayed in bold and add ** before and after the text like Google, it breaks the link's image.