I know Chris Webster (at JPL) well and have discussed the TLS instruments he builds at length. They have more in common with the MIRO instrument on the ESA Rosetta spacecraft (I was a co-investigator on that instrument) than with sector or quadrupole mass spectrometers.
Mass spectrometers have relatively poor mass resolution but can measure atoms or molecules of any mass over their design range. Hence they are called "survey" instruments. If you're not sure what species you're going to find, you use one of these to get a wide cut at the atmosphere's composition. If you put a pyrolyser at the inlet you can volatilize liquids and measure those, or thermally break down solids and measure their decomposition products. It's a "broad brush" approach.
The TLS looks at how much specific absorption lines of specific molecules absorb a laser beam propagating through a sample of gas. The amount of absorption tells you how much of that species is in the gas mixture. You have to measure multiple lines for each species to sort out molecular abundance from temperature. Temperature affects the population of molecules in the specific energy states—energy of rotation, or vibration, or both—that give rise to those lines.
But the wavelength of one TLS laser "channel" is tunable over a limited range, and you can have a limited number of channels: each channel adds mass to the instrument and takes more power. So when you design the instrument, you have to tune the channels you can afford (in cost, mass, power, data volume—all those pesky limitations!) to cover those molecules you're really, really interested in, and are confident you will actually see when you get to the destination.
To measure isotopic ratios in something like methane, you have to have channels that will get at least a couple CH4 lines, where the C is "normal" 12C and the H's are "normal" hydrogen, not deuterium. To get carbon isotopes you have to add coverage at the wavelengths of 13C-H4 lines, 14C-H4 lines, etc. (at least two lines each), and those wavelengths are significantly different from those of the 12C molecules. To get D/H you have to add coverage at the wavelengths of 12C-H3D lines. So you can quickly use up all your instrument's mass, power, etc. allocations chasing this one objective. If it's really, really important, you might do that. But when Curiosity was designed, nearly ten years ago, there wasn't that much importance attached to it.
So far the data discussed in the Science paper indicate that finding methane on Mars is highly variable and rather unpredictable other than a mild seasonal correlation. At the time the Curiosity TLS was designed it was a matter of debate as to whether methane had actually been detected at all. And Kevin Zahnle of NASA Ames even suggests the methane detected might have come from Curiosity itself, though Chris doubts that. But uncertainty about whether you would detect methane at all is another argument against chasing that objective.
It might be different now.