The "action" part is fine. The typo is using the word "check" rather than "save". As the rules say "a saving throw represents an attempt to resist a spell". Taking the spell as written, the halfling's "Brave" ability does nothing, since it gives advantage on saving throws against fear, not ability checks against fear.
I don't think it is a typo. In 5E you can use an action to do a skill check. You can't use an action to make a save. I think that is the reason it is a skill check and it is a check on every similar spell I could find.
Halfling Brave would work on the initial save to avoid the effects, but it would not work on the skill check to break out of it. This is the same as Gnome cunning. It would work on the save but not on the skill check if you fail the first save. It is not just this spell either. For a Gnome, it would be exactly the same mechanic on other spells with a save and subsequent actions to break - things like Phantasmal force which is also a Wisdom save to resist and then a check to break and Detect Thoughts which is a int save to resist and an int check to break.
It is also the same for Monsters with Magic Resistance that you target with any of these spells - advantage on the save to resist, no advantage on the check to break.
I think it is not a typo since other spells work the same way. Here is a list of those I know of:
Mionor illusion, Disguise Self, Silent Image, Phantasmal Force, Detect Thoughts, Web, Earthen Grasp, Ensnaring Strike, Evard's Tentacles, Otiluke's Sphere, Maze
If it is a typo, then it is a typo that is widespread and exists on all those spells. On the other hand I can't think of any spell in the game that uses an action to break and is a save on that action.
