Is it permissible to review lessons inside mosques?

The basic principle regarding reviewing lessons in the mosque is permissibility, unless something arises to prevent it. This includes, for example, doing so in a loud voice beyond what is needed. The prohibition intensifies if it leads to disturbing those praying, reciting, or remembering Allah, due to the Prophet's (peace be upon him) saying: "And let not some of you raise their voices over others in recitation."

Imam Malik disliked raising one's voice with knowledge in the mosque.

Therefore, there is no harm in reviewing lessons in the mosque, provided there is no disturbance or raising of voices, and that what is being reviewed is beneficial and useful, while observing the manners of the mosque.