[Vuejs]-Leaflet map remains present when modal is active. Why?

Without seeing this in action I can only guess. But most likely the modal, the dark overlay behind the modal, and the map all have their css position set to absolute or relative and a number assigned to their css z-index.

The z-index of the map is likely higher than that of the modal or the background overlay, causing it to appear in front. The solution, if this is the case is to modify the z-index values to get them in the right order.