What should I do about a hole in my dryer hose?
If your cats tore a hole in it, it has to be flex hose. 

Do yourself a huge favor and replace every inch of flex hose with solid metal dryer vent. Flex hose collects vast amounts of lint that get past the lint filer and is impossible to clean effectively (not to mention being delicate enough to be torn by cats.)

As a one-time event I would not be overly concerned about the dry-cleaning sheet. But I would definitely scrap the hose and replace it with solid metal before using the dryer again.