this is called a 'fallacy' in theological terms, as the 'napkin' used to wrap bodies was not at all similar to the one used many centuries later to wipe mouths after eating. it would be like a story saying Jesus told a parable about a lost airplane; it would not be relevant to the people who lived at that time.
there are many many other passages in the Bible that prove that Jesus will return again in glory, so we don't need this little story to confirm our faith. it is a nice story, but not accurate.
what our priest explained is that lazarus, when he rose, came out wrapped in his grave clothes, and those who were there had to take them of him. he would need them again later when he died again.
Jesus' grave clothes were folded up neatly ready to be packed away because he didn't need them again. He came out without his grave clothes, as He defeated death and no longer had any connection with death.