The $$$ symbols which are displayed in the hyperterminal when AT+WDWL command is given are nothing but the NACK control characters which are sent by the XModem or 1KXModem protocol to tell the sender to initiate the data transfer. In your case, were you able to download the file properly without receiving the $$$ symbols?
In case, you were able to download, it means that the NACK control characters were send but you were not able to see them because in some utilities, the control characters (like NACK) are not displayed but actually they are received.
In Hyperterminal too, if you change the FONT from “TERMINAL” (which is default) to COURIER, you will not see the $$$ symbols but will instead see the ||| symbols.
Even in TE, if you given AT+WDWL command, you will see that ||| symbols appear in the data window (though you will not be able to send the dwl file from there as TE, does not implement the XModem/1kXModem protocol which is required by the module to get the file from the sender).
Open AT Fan.