As with all the other Digi boxes, it seems that the Digitakt II is no exception and class compliant audio doesn’t work on Linux.
I get distorted audio when I play something back from my computer. Recording the Digitakt II itself seems to work fine, just like with the other Digi boxes.
Do the samples you audition align with the DT audio format, iirc 16bit 48k ?
Otherwise you could potentially be hearing poor sample rate conversion from the host device.
This is how I tested. I get the same distorted sound as with my other Digi boxes. The same command produces a clean sine wave on my speakers.
~ speaker-test -Dhw:2,0 -tsin -c2 -r48000 -FS32_LE
I never had problems in Linux with my Elektrons. Are you using pipewire? If not, go for it 
It’s possible that the sample rate of your system is set to something else than 48kHz which would explain the problems.
I am using PipeWire. It was working at some point (years ago). PipeWire itself would be using ALSA to actually access the device so by testing with `speaker-test´ I basically removed as many middle man as possible.
Just out of curiosity, can you try running that command? Do you get a nice and clean sine wave?
As @frekvencia said, this is a problem that affect all the boxes but depends on the USB port and hub and the other devices that are connected to it.
Slightly disappointing to see that this is still an issue.
Link some other threads for reference.