A few days ago I submitted a very similar response to an earlier question about warts, so I apologize for repeating myself but this is something that needs to be better understood.
It is extremely unlikely, even close to impossible, that HPV (Human Papilloma Virus) of the type to cause warts could ever be transmitted from a table cover or towel. Were this to happen it would have to be a real fluke, caused by the concurrence of several coincidences all at the same time.
Forget about getting Genital Warts this way!
Intimate contact, skin to skin, (or maybe "wart to skin" is a better expression) is needed to transmit Genital Warts and Genital Warts will not grow on dry areas such as the hands. They require moisture to flourish so the most common areas are the mouth and anal areas, and in women the vulva and vagina and in men the shaft and meatus or opening of the urethra on the penis.
Common warts on the hands and feet are also caused by HPV's though they are not the same type of HPV's responsible for Genital Warts. Nor will Genital Warts grow on the hands and feet.
There are are about 60 different types of HPV recognized, and of these, only about a third are considered to be sexually transmissible. And of those HPV's that are sexually transmissible, only a few are responsible for producing warts though they all may infect the body, some w/o presenting any symptoms.