There must ALWAYS be some kind of low-pass filtering whenever you convert analog audio to digital. Any significant signal energy (from whatever source, including noise and distortion) at or above 1/2 the sampling frequency will cause distortion that's potentially quite nasty-sounding, since it's completely unrelated harmonically to the original sound.
In the early days of professional digital audio (ca. 1979) the sampling rate for most of the available recording equipment was fixed at 44.1 kHz, and the filters cut off the high frequencies right at 20 kHz. The entire response "dropoff" (typically 60 dB or greater!) thus occurred in the very narrow range between 20 kHz and 22.05 kHz. This steep cutoff required extremely complex filter circuits, which were implemented entirely in analog back then. Thus the filters were generally the weakest link in the audio "chain", with limited headroom, severe impulse response / group delay problems, plus a tendency to drift with temperature and the aging of their components. Also, they were damned expensive.
When recording equipment with higher sampling rates came along, for most people who were serious about audio quality, the main advantage was that the filters could be designed to cause less harm to signals at and below 20 kHz. That's what this menu is ultimately about, and it may well be worth paying some attention to the choices. Absence of pre-echo and low group delay are both desirable sonically--particularly the former, which is readily audible on specially-constructed test signals and occasionally even in real-world recording, e.g. certain percussion instruments if they're cleanly miked. So I would choose those features--"short delay 2" on this recorder--unless there was some reason to expect significant signal energy above the cutoff frequency, in which (highly unexpected) case I would choose the default "short delay 1".
In some special applications (e.g. acoustical measurements using miniature models of an architectural space; some sound effects) there's a legitimate need to preserve signals above 20 kHz--but only because after the recording has been made, the playback clock is slowed down so that those signals drop into the audible range.
--best regards