Does the retention of a person's image in one's mind during prayer, after having dealt with them or seen them, constitute polytheism (shirk) or an illness, and how can one rid oneself of it?

What you mentioned is not shirk (polytheism); rather, it is from Satan, who seeks to prevent you from turning to your Lord with presence and devotion. Satan is keen on corrupting worship, especially prayer, and he whispers to the worshipper, reminding them of things they had not remembered before. If Satan whispers to you during your prayer, seek refuge in Allah from him and spit lightly to your left three times, as 'Uthman ibn Abi al-'As did. This devil is named Khanzab. The worshipper should be present with their heart and be humble in their prayer as much as they are able, for the reward of the prayer is proportionate to the humility in it.