I have a mid-level BBEG with Telekinetic Grasp.

Telekinetic Grasp. The Draco Deadnaught chooses one creature it can see within 100 feet of it weighing less than 400 pounds. The target must succeed on a Strength saving throw (DC 15) or be pulled up to 80 feet directly toward the Deadnaught.

This villain fought the party and was soundly defeated. The Cult of the Dragon members that built it recovered the remains and is working on a version2 for revenge.

The party's  goliath barbarian has a magic battle axe that was particularly damaging to my Draco Deadnaught. QUESTION!

How would YOU handle Telekinetic Grasp VS the barbarian's raging grasp to YEET the battle axe away from him? THANKS!

Recurring villains are fun because you have the opportunity to actually tailor against the party. Be sure to make note of what they choose to tailor against - in this case the axe - and avoid tailoring against new things since the previous encounter! In my case, I have an Ettin artificer who will eventually make himselves into the Juggernaut. First step, a pair of helmets to protect against mind magic! Next time she plays "Hold Monster", he will tap his helmeted head and say "not today, girly, not today".

Now, I don't know of an ability called Raging Grasp, but the way I would handle it is that the axe is being flung, with or without the barbarian. Alternately, the axe is being taken, dragged to them. Think of the conflict in the barbarian players mind if they approach, only to find they are trying to drag the axe from their grip, the pull getting stronger the closer they get? Should the ycharge forward with the axe? Should they run with it? Should they abandon it and use a different weapon?

I just meant the barbarian's increased grasp I imagine they would have while raging. Would this be a contest roll? Or would the already set STR DC 15 stand, but instead of pulling the player to it, my villain would be focusing on ripping the item from the player? Thanks!

And yeah, reoccurring villains are THEE BEST as my players turn the corner into 6th level and higher! 

Well, a barbarian has advantage on strength checks when raging so that extra grip is already accounted for, if they're angry enough!

I would make it a staggered check. DC15 to hold onto it. DC 20 to not move. Move 5ft for each 2 points they fail by (up to 10ft.). So 0-14 loses the axe, 15-16 moves 10ft forward, 17-18 moves 5ft. forward, 19+ doesn't move. So technically DC 19 to not move, but you get the gist!

YEEE-OW!! Ya nailed it! That's a mechanic I can get behind at our table. Thanks!

if you want a mechanic to really make them make decisions, have them simply raise the axe upwards. That way the barbarian is not getting a free ride closer, and they will have to choose between trying to free the axe, or leaving it be so they can get into the fight!

Noted! Very true! This villain can fly, the barbarian can't. Great point!!

Quote from Cementario >>

I have a mid-level BBEG with Telekinetic Grasp.

Telekinetic Grasp. The Draco Deadnaught chooses one creature it can see within 100 feet of it weighing less than 400 pounds. The target must succeed on a Strength saving throw (DC 15) or be pulled up to 80 feet directly toward the Deadnaught.

This villain fought the party and was soundly defeated. The Cult of the Dragon members that built it recovered the remains and is working on a version2 for revenge.

The party's  goliath barbarian has a magic battle axe that was particularly damaging to my Draco Deadnaught. QUESTION!

How would YOU handle Telekinetic Grasp VS the barbarian's raging grasp to YEET the battle axe away from him? THANKS!

 I'd first check if the Barbarian was an eligible target for Telekinetic Grasp. Goliath tipycally weigh between 280 and 340 pounds, add in all gears likely get it over 400 lbs.

If not, then the Barbarian would have advantage to the Strenght saving throw due to Rage feature. But being pulled and stay closer to an enemy is usually what melee characters want so wether it save or not, it would end up there, unless the creature is in the air.... If your BBEG is a Draconian Dreadnought  flying 60 feet high when using Telekinetic Grasp as a pull-and-fall tactic, then no character wants that.

Totally. Yes, this villan is a fey-powered, mummified Draconian Dreadnought. So lift n drop is going to be a new focus vs the party come round 2.

In other options: Suppress Magic (From the Conclave Dryad)

Suppress Magic (Recharge 5–6). The dryad targets one magic item it can see within 120 feet of it. If the magic item isn’t an artifact, its magical properties are suppressed for 10 minutes, until the dryad is incapacitated or dies, or until the dryad uses a bonus action to end the effect.

Consider it an anti-magic item laser.

OooooohWEE!!! 

The BBEG of my party is a Blue Dragon collecting intelligence on Draco Lich rites w the help of a hag coven with an axe ta grind against the party. 

Suppress magic is a great idea especially because the barabarian's battle axe was a gift from the party's patrons hoarde. A Copper Dragon currently in a friendly-ish powerplay w the bbeg blue dragon!

So any power ole Sparky's mummy Draco deadnaught  "troop" would have to snuff his party's toys would really get under his copper scales!

 Just watch out for how much tweaking you do to counter the party.  There's a fine line between "making a villain more challenging" and "making the players feel like you're unfairly penalizing their characters."  And it's especially fine when the character in question has very few options in combat, like a barbarian.

That's a very true point. Half the players are DMs in other campaigns so that would be pretty transparent.