It won't hurt the battery. The difference between the adsorbed charging capacitor pen and the non-adsorbed charging capacitor pen is only that an additional magnet is added, and the purpose is to fix the capacitor pen with magnetic attraction.
This adsorption permanent magnet, its own magnetic field is fixed, not alternating magnetic field, so it will not have any impact on the capacitor pen circuit, let alone damage to the capacitor pen battery.