How can Skype track downloaded file on the file system?
I don't use Skype but I suspect the fact it came from Skype is stored in one of two places. To find out, copy a Skype download to your Home directory and start Terminal. If your file is called, say, photo.jpg, you would run:

mdls photo.jpg


to list the metadata and something in there will refer to Skype or its bundle identifier.

Alternatively, run:

xattr -l photo.jpg


and see if Skype is listed in its WhereFrom attribute.