In Jain practice, there isn’t a single universal rule about touching sacred objects like a Namokar mantra poster during menstruation. Traditions vary between Digambar and Śvetāmbara communities, and local temple customs can also differ.

What is commonly observed:

• Many households and temples prefer that items considered sacred be handled by someone who is not observing ritual impurity. This can mean that a person on period may avoid directly touching the poster.
• If one must handle it, people often use a clean cloth or cover (a barrier) before touching, or have someone else handle the item.
• Some communities allow touching with proper cleanliness and then washing hands afterward, but the exact practice can depend on local tradition.

Practical guidance you can follow:

• Check with your local guru, temple priest, or community practice to know the standard in your area.
• If you touch the poster during menstruation, do so with a clean covering, or have another person handle it.
• After handling, wash your hands with water and consider performing a quick purifying routine as per your family tradition.

If you’d like, tell me which Jain tradition (Digambar or Śvetāmbara) or your local temple you follow, and I can tailor the guidance more closely to that practice.