If the dome was created by an object (like a magic item) as a direct effect, it cannot be dispelled by Dispel Magic.
If the dome was created by a spell cast from a creature or magic item then it dispels the effect entirely and completely (no returning) if you succeed.
Dispel Magic only affects Spells. This could be a spell cast through a magic item like a Staff of Power or any caster, or monster with innate spellcasting. It can dispel a spell from a creature (like Mage Armour), object (like Magic Aura), effect or spell-created object (like Magnicent Mansion or Tiny Hut). The spell you are dispelling must have an active duration - spells that were Instantaneous cannot be dispelled even if the spell effect remains.
Dispel Magic does nothing to other magical effects that are not a spell, like a Staff of Woodlands being a tree, or fire resistance from a Ring of Fire Resistance.
If the globe is caused by somebody using a Magic Item with the effectof creating the globe then it cannot be dispelled. If the globe is caused by somebody using a Magic Item which casts a spell that produces the globe then it can be dispelled. If the globe is caused by somebody casting a spell to create the globe then it can be dispelled.