Gaussian blur is your friend if you wanna send a death note, I guess.
Also, I doubt you can get conclusive evidence from a single letter. Luckily, your average random note has lot of them, even duplicated ones. I would carefully align and average out as many capital A’s as I had, and work with that.
You missed the explanation above why you're wrong, at least on consumer non-PostScript printers. Most cheap printers nowadays passes the buck of rasterisation to Windows (and its horrible, security headache spooler). You can even check if which is which: in Windows 10, open Settings, then Devices, select Printers & scanners, select [your name of printer], press Manage, press Printer Options (not Printing options), open the Advanced tab and then click on the Print Processor... button. If it says "winprint" then Windows handles the rasteriser.
I think they meant something like "ink smears".
Pinpointing a version of Windows, if it was printed from a stock OS font, could be as simple as comparing tiny differences in the vector files and knowing if one pixel would rasterize at 60% black versus 50%. To the extent that the rip goes through a graphics card, it would be knowing whether that card rendered the 60% as 58% or 62%.
I'm pretty sure if you scale it down, the printer driver will do an extra layer of downsampling and add its own anti-aliasing; but the printer hardware doesn't do that, it just sprays the dots it's told to spray, and in general the drivers replicate the pixels that are sent from Photoshop or in this case, MS Word, which uses something like QuickDraw used to be on a Mac, an embedded system process, to rasterize the fonts.
Prior to this it had never occurred to me. But yeah, more randomness. Noise filter and blur, then a bit more noise, then photograph it, print the photo, scan it on another device, put it in the washing machine, leave it on the porch for a week and repeat.
Could also be by design, similar to printer identification dots. Have the artifacting vary every so slightly from one GPU to another. Then again, I feel (emotional statement, not of fact) that this would be known by now if it was a thing.
So...evidently from a sample of me, I can tell from which monitor a screenshot was taken...
Most cheaper printers (esp. on Windows) use the GDI protocol for printing. These printers only know how to print rasterised images, so the document is rasterised by the OS/Print driver and only this final rasterised image is sent to the printer. This is different from higher end PCL/PS printers where the document is translated into a page description language and the printer is (partially) responsible for rasterising the final document for print.
Since Windows uses the GPU to render fonts I wouldn't be surprised if the same code is used to rasterise the fonts for GDI printing.
That being said I'm very surprised they can identify the GPU just from that, unless there is some specific bug in the driver for the card which produces an obvious font rendering artefact.