If you look at their current sourcing it's fine. They're not cutting apart glaciers, they're gathering it from parts that have calved and will just melt apart regardless.
Greenland has a right to sell their natural resources as much as anyone else, and the sad thing is this admittedly ludicrous enterprise is more profitable for less environmental damage than most things.
The problem is all the carbon that is emitted to transport the ice from Greenland halfway around the world for no other reason than bullshit marketing.
People forget it's not just the shipping itself. First of all, ships just like every other vehicle need more energy to move the heavier they are. Secondly the ice needs to be cooled for most of the trip and portable coolers are real energy guzzlers. So without doing the maths transporting ice from Greenland to Dubai is much more harmful than ships with empty containers on the same way.
The first point doesn't hold though. it is always better to have a ship run with cargo than without, in terms of efficiency. Afterall the point of the ship moving is to transport cargo.
For the cooling i am also sceptical. It was common all over Europe to trade with ice cut out of glaciers and frozen lakes until the invention of the cooling pump made electrical fridges a thing. If you store the ice in somewhat well insulated containers, it will cool itself quite decently for long travels. Icecellars were common to hold Ice that was collected in winter and lasted for cooling all throughout the year even in the mediteranian areas.
I also find this business obscene, but i do not see, that it would be more harmful, than sending empty ships around the world.
It is more efficient to have a ship moving with cargo than without, but that doesn't mean there aren't additional emissions. The ratio of profit to effort is just higher because there is some profit as opposed to none. You wouldn't load a ship up with useless mass you can't sell just so you're shipping something.
Your argument is like always running the heater in your car because that way the engine heat is at least used for something. Yes, technically the efficiency goes up because more of the energy in the fuel is harnessed. But that doesn't mean the fuel usage or emissions are any lower, and in the summer the heater doesn't do you any good either.
International overseas shipping is actually pretty carbon efficient as transport goes.
Hell they're actually pretty down for efficiency improvements in shipping, to the point where people are just straight up talking about bringing back sails because... Well, why not? It's free energy.
It's not necessary but you compare this to crypto or deliberately inefficient vehicle design and it's just not something to get upset about.