You can bring home only the small towel packed with a tooth brush.
In guest rooms at Japanese style inns, at both Ryokan and Minshuku, a set of toiletries including a toothbrush, a toothpaste and a small towel is usually provided per guest. They are often packaged in a plastic bag or pouch. You are allowed to take home this types of small, thin towel, which usually has inn’s name printed on it.
The towel in the package is for use when taking a bath. Japanese inns usually have a large public bath “Daiyokujou” and guests are to bring the small towel and the bath towel from their room to the bath. If the towel comes with a plastic pouch, you can use the pouch to carry the towel to Daiyokujou.(Soap and shampoo are provided in the public bath bath)
How do you know which towel is OK to bring home?
The towel that you are allowed to take home is only the small, thin towels. Bath towels and face towels provided in washrooms are NOT allowed to take them home.
If you are not sure which one is OK, you may ask a staff at the inn with saying;
Kono Towel, moratte yoroshii desuka?
(Is it OK to have this towel?)
*Small hand towel is called Tenugui in Japanese, but the English word "Towel" is more used now.
Get the towel and make the best use of it
Most Japanese guests don’t take them home, probably it is because having to carry the wet towel is bothersome, or some of them even don’t know if it is OK to get it or not.
Since this towel is disposed of after use, it is recommended you get the towel and make the best use of it. The towel actually comes in handy on a trip, when you take an Ashiyu foot bath etc. The towel also can be a souvenir from Japan as the Kanji characters printed on the towel look nice.