Trello isn't able to accept local file links, because your browser isn't able to open them. We have some more information about that here: http://help.trello.com/article/1040-why-cant-i-open-file-links
In this case, when you try to paste a string of text that starts with two backslashes, the first one is being removed because Trello is interpreting this as purposeful formatting. You can enter a backslash before a string that Markdown would otherwise auto-format in order to preserve your chosen formatting, and that's what Trello is seeing here: http://help.trello.com/article/821-using-markdown-in-trello
One workaround is to paste your local link inside of triple tickmarks to mark it as a code block, like this:
This will stop that first backslash from being removed!
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