That's not sufficient
You may have to get rid of some circuit built into the device, and add your own current control.
You may be happier with 1-2 bare IR power diodes and a transistor and current limiting resistor. For IR remotes the diodes can not have any built-in current control!
There are a lot of possibilities in between the tiny battery-poweredLED in a typical remote, and the multi-watt monster that you linked.
The usual solution is to use several somewhat larger and higher-powered LEDs like you see here: https://www.adafruit.com/product/73
It would be helpful if you could give us more information to work with:
What are the brand and model number of the remote and the TV (assuming it's a TV)?
What's the maximum distance at which the remote works now?
What's the distance at which you want it to work?
Have you tried fresh batteries?
Anyway, depending on how much improvement you need, it might be possible to just replace the IR LED with one that concentrates the power into a narrower beam that will project farther (although you have to be more careful about pointing). But other than that, you would need the schematic for the remote, or at least figure out that part of the circuit that drives the LED, before we could tell whether other changes might be possible.
Of course you can build a remote, but that would be a lot of work, and the final result might not be easy to use. A better option might be to find a "learning" universal remote that has a better range, if you can find one, or possibly find or build an IR repeater that you could install midway.
Gone are the days when remotes used a 9volt battery and four IR LEDs.
One of my remotes did more than 60 metres when aimed carefully.
You could turn off the neighbour's TV with it
Leo..
Yes, it's amazing how well they work now. They push something like an amp through the LED, with a 1 ohm resistor, or no resistor at all, and nothing blows up.
The cheap red lasers from China have a huge amount of IR splash so they can be used in an application like this, hence the beam can be easily aimed at an IR receiver.
All I see is two IR LEDs with CL resistors, switched with a fet.
If I would have build this I would have used a 2-transistor constant current source.
It works, but not with a fixed/stable/supply-independent LED current.
Not what I expect from Adafruit.
Leo..
Do constant current sources respond quickly enough to run a 40kHz IR RC signal through?
In any case, that would seem like overkill given 100mA-200mA LEDs and a regulated voltage source. And.... $4...