Can you use an associated object gathered by someone else to teleport

By RAW, an object is a single designated thing that isn't alive. In my opinion RAI extends to obvious containers.

The teleport spell states (emphasis mine):

This spell instantly transports you and up to eight willing creatures of your choice that you can see within range, or a single object that you can see within range, to a destination you select. If you target an object, it must be able to fit entirely inside a 10-foot cube, and it can’t be held or carried by an unwilling creature.

This wording indicates it only applies to a single object since it does not say all objects. It also makes no exceptions for containers and their contents.

For example, if you could transport anything in a container all you would have to do is build a makeshift 10 X 10 X 10 wooden cage and call it a large box. Then you could teleport 1000 cubic feet of whatever you want because you targeted the container.

Personally, I would allow transporting obvious containers like chests, bags of holding, boxes, jars, etc because that seems in keeping with the intent of the game mechanics. It also avoids the unnecessary confusion and ceaseless arguing over just how many separate objects make up a single carriage.

I would say that common sense needs to prevail. If the contents of a table would fit in a standard chest, there's no real reason to prevent players from designating the table or shelf as a container for the purpose of transport. Especially if you're willing to let them just throw it in a Santa Claus bag and transport that anyways.

Now, if the players were trying to be deliberately game breaking with it, you can always have fun. Let's say they stack the treasure eight feet tall on a small bench and transport it. When they arrive, the mound of treasures topples, and riches are scattered everywhere. Small street urchins, poor folk, homeless beggars and Paul's girlfriend are all seen sprinting in to scoop up as much as possible. The player's are able to recover X % of the treasure before the rest disappears, and the guards come by and fine/imprison them for starting a riot.

That's just my opinion though. I don't mind people bending the rules a bit to do some ridiculous stuff, but I bend back a bit to show them I'll be just as ridiculous in response.

Not directly

he's claiming that since he can see it, it's known to him

The player wants to teleport an item inside the dragon. If so, he can't see the destination point.

Moreover, "the destination <...> known to you" in the context of this spell means some kind of a place, like a room, a square, a meadow, etc. Otherwise, a PC could be teleported inside a mountain rock due to the mishap. See the examples from the Familiarity column description:

such as a book from a wizard's library, bed linen from a royal suite, or a chunk of marble from a lich's secret tomb.

But the main mechanical reason for this not to work is the fact that killing in D&D is meant to be done through dealing damage (it's a game term, any damage dealt implies damage type and a number being subtracted from hit points). If a spell can deal damage its description always says that. For example, the Catapult spell explicitly says you can deal damage with it:

When the object strikes something, the object and what it strikes each take 3d8 bludgeoning damage.

The Teleport spell doesn't say it deals damage (besides the Mishap side effect, that might deal damage to teleported creatures). See also What is the source of the "spells do only what they say they do" rules interpretation principle?

As the DM, you resolve this by saying "no, you can't teleport an item inside a living creature, it is a limitation of the spell".

However, the player might try to teleport a rock above the dragon. I'd say it's possible to deal damage in this case — you can use rules for a similar trap to adjudicate this:

Collapsing Roof

When the trap is triggered, the unstable ceiling collapses. Any creature in the area beneath the unstable section must succeed on a DC 15 Dexterity saving throw, taking 22 (4d10) bludgeoning damage on a failed save, or half as much damage on a successful one.

See also How might the weight of a falling object affect the damage it causes?