Rav Yosef Shalom Elyashiv (contemporary) writes (listen to audio recording for precise citation) that it is proper during Pesah to use different books for Pizmonim and Birkat Ha’mazon. The Pizmonim and Birkat Ha’mazon books and cards used during the year often have food on them, as they are frequently brought to the table, and it is therefore proper to put them away for Pesah and use different books during the holiday. It may be too costly for some to purchase new Pizmonim books for Pesah, in which case they should be thoroughly cleaned and checked for Hametz, and may then be used during Pesah.
Books that are not normally brought to the table do not have to be checked before Pesah for Hametz. However, if a person has books that he occasionally brings to the table, he should ensure not to bring them to his table on Pesah, because there might a crumb in the book that could fall onto his plate. Hametz on Pesah is not subject to "Bittul" ("nullification"), meaning, it is forbidden even in the smallest proportion, and one should therefore ensure not to bring to the table books that might have Hametz crumbs in them. If he wishes, he can put down a towel or some other material on the table and then place the book on the towel.
One should ensure to use a tablecloth to cover his table whenever he eats on Pesah. Even if the table has been cleaned and one eats cold food, he should nevertheless make sure the table is covered. Rav Elyashiv even advises using a second covering in addition to the tablecloth, but one should at very least ensure to have a tablecloth so he does not eat directly on the table.
Summary: Birkat Ha’mazon and Pizmonim books used at the table during the year should not be used on Pesah. Books in general do not need to be checked for Hametz before Pesah, but a book that has occasionally been brought to the table should not be placed directly on the table during Pesah. One should use a tablecloth anytime he eats during Pesah, rather than eat directly on the table, even if it was thoroughly cleaned.
