Impossible to say

We have, effectively, three points of information. First,

• the entry on the disarm variant rule states that

  A creature can use a weapon attack to knock a weapon or another item from a target's grasp.

  and the entry on the battlemaster’s disarming attack lets you

  When you hit a creature with a weapon attack, you can [...force...] it to drop one item of your choice that it's holding.

So the question becomes whether or not a shield is an item that you “hold” or is in your “grasp.” To answer that, we have two more points to consider:

• The entry on shields says

  A shield [...] is carried in one hand.

• While weapons don’t usually require an action to draw, as the Use an Object action states that

  You normally interact with an object while doing something else, such as when you draw a sword as part of an attack.

  shields instead require their own separate action to “don,” as indicated by the “donning and doffing armor” table on page 146.

These last two imply but do not state completely opposite answers to the question of whether or not a shield is a held item that can be disarmed. Neither one of them explicitly or conclusively says one way or the other, but “carried in one hand” suggests that the shield is merely held, while “donning” and taking extra time to do so implies that the shield is strapped on.

We do not have enough information to definitively state an answer one way or the other.

You can pick it up.

The question you quote is correct that your enemy can just pick the item back up, but they have to do it on their turn. You can pick it up on the same turn you do the disarm, though (PHB 190):

You can also interact with one object or feature of the environment for free, during either your move or your action.

In the table on the same page, labeled "Interacting with Objects Around You," one of the options is

pick up a dropped axe

Your disarm is part of your action, so you can pick it up alongside this action. Now that you've stolen the disarmed item, the enemy has to disarm you to get it back.

You can stash it.

It's a bit ambiguous whether or not you can stow the item in the same round without expending an action on it. The same page in the PHB states,

If you want to interact with a second object, you need to use your action.

Since picking up the item and stowing it is interacting with only one item, one could easily argue that the entire thing falls under a single item interaction. If that is the case, then your enemy would have to do something else to get the item back, as you're no longer holding it. Alternatively, since it's two different actions you're taking with the same item, a DM could say that it costs an action. It's ultimately up to the DM anyway:

The DM might require you to use an action for any of these activities when it needs special care or when it presents an unusual obstacle.

Personally, I would rule differently depending on the item. If it was a small orb or something, I would let a character put it away without a second item interaction, but if it was a warhammer, I would require an action.

Your teammates can damage it.

If you have a teammate that goes before them, they could also pick up the item or attack it or something before the enemy can retrieve it.

For example, Fire Storm states,

The fire damages objects in the area and ignites flammable objects that aren't being worn or carried.

and therefore would damage or destroy the object once it's dropped. Similar spells like Fireball have similar wording. Indeed, if someone were to cast Fire Storm on the square in which your enemy was standing, the disarmed object would catch on fire as soon as it is no longer carried.

For completeness, the PHB does allow targeting objects with attack rolls. On pg. 194, in the "Make an Attack" section, the first option is:

1. Choose a target. Pick a target within your attack’s range: a creature, an object, or a location.