Some non-Catholics, and your friend seems to be one of them, believe incorrectly that the Catholic Church teachs we can somehow work our way to heaven by our righteous deeds. By repeating the phrase about the filthy rags, I think your friend, in her way, is trying to counter that truly erroneous teaching, as St. Paul did when he wrote in Ephesians 2:8-9, “For by grace you have been saved through faith; and this is not your own doing, it is the gift of God–not because of works, lest any man should boast.”
The problem with the phrase about the filthy rags is that it gives the impression that righteous deeds are to be avoided and this is clearly not true. As St. Paul immediately says in Ephesians 2:10, “For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.” Or, as St. James said, “What does it profit, my brethren, if a man says he has faith but has not works? Can his faith save him? [The answer to this rhetorical question is: No!] … So faith by itself, if it has no works, is dead.” (James 2:14-17)
You may wish to remind your friend that “the righteous deeds of the saints” are not filthy rags but “fine linen, bright and pure” and it is with this fine linen that the Bride of the Lamb will be clothed at their marriage, according to Revelation 19:7-8.