[jonaz]

Much thanks to @iveskev from the Desk.com “WOW” team for this answer:

If you do {{'now'}} it returns the string “now” not a timestamp for the current time. So if you do {{'now' | minus: 604800 }} it returns “-604800” not the current unix time minus 604800. When you use the date filter, then liquid picks up that you are referencing the current time and outputs the time as a string. However even if we get ‘now’ to output the current date, we are still subtracting from a string and so will be returned with “-604800”. The only time that math on a string works correctly is if the sting is only a number.

So in order to get the correct date we first have to get the unix timestamp for now, do the subtraction, then reformat to the desired formate. You can use %s to get unix time. So to get the current time in unix it would be:
{{'now' | date: '%s' }}

At that point you can then do the subtraction and then format the time in the correct way. We can do this all at once in the following statement:

{{'now' | date: "%s" | minus : 604800 | date: "%b %d, %Y %I:%M %p -0500" | uri_encode | replace:"+","%20"}}

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