What is the ruling on the imam sometimes omitting the letter "hāʾ" (ه) from "ḥamidah" (حمده) in his saying, "Samʻa Allāhu li-man ḥamidah" (سمع الله لمن حمده), and what should the worshipper do?

The congregant is not liable if the Imam does not pronounce the letter 'Hā' in "Sami‘a Allahu liman Hamidah" (Allah hears those who praise Him), because the Imam's mispronunciation outside of Al-Fatihah does not affect the congregant's prayer. If you ascertain that he does not pronounce the Tasmi‘ (saying "Sami‘a Allahu liman Hamidah") completely, then inform him so that he may pronounce it, because the Tasmi‘ is among the obligations of prayer or its emphasized Sunnahs.