The CS4392 and CS4272 DACs in particular sport fairly high-order noise shaping and even the circuit suggested in the CS4392 datasheet isn't really adequate for taming their out-of-band noise (no surprise because it was retained from the CS4391 with a lower-order modulator)... and I suspect many cheap audio interfaces have even more basic filtering than that, close to none in some cases. There have been other problems with this, e.g. the Arturia Minifuse headphone output managed to upset Amir's AP at lower signal levels (i.e. higher input gain).
Back when the CS4392 was designed at the start of the 2000s, this design choice meant that they could squeeze midrange audio interface level dynamic range and good low-level linearity out of a compact, relatively inexpensive chip design. I think it uses a 5th-order modulator, which is among the highest ever used in a DAC. (There were some ADC designs with 7th-order ones like the CS5396/97, which was a challenge to make work in the first place, but it's feasible because the out-of-band noise gets taken care of by the decimating filter chain.)
I wouldn't expect much help from the manufacturer in such an obscure use case. Tape was dead even back when the DAC was designed. If the MPX filter doesn't seem too heavy-handed, just leave that on. As an aside, don't you have any half-decent (Realtek) onboard audio at hand? Even a lowly ALC892 has at least 20 dB more dynamic range to offer than any compact cassette ever will, and a lot less out-of-band noise I bet. If there still is some periodic passband ripple in the ADC filter that you're concerned about, just record at 192 kHz to make it insignificant, or stick with the Behringer for recording if clock sync is not a concern.
BTW, the Behringer UMC HD series is about due for a redesign anyway. They're one of the last stubbornly sticking with a +5V single supply for their analog section.