curl tem uma opção,
Da página de manual!
-z/--time-cond
(HTTP/FTP) Request a file that has been modified later than the given time and date, or one that has been modified before that time. The date expression can be all sorts of date strings or if it doesn't match any internal ones, it tries to get the time from a given file name instead! See the curl_getdate(3) man pages for date expression details.
Start the date expression with a dash (-) to make it request for a document that is older than the given date/time, default is a
document that is newer than the specified date/time.If this option is used several times, the last one will be used.