I think it comes from the so called "Auslautverhärtung" (final-obstruent devoicing). It means, that in German (among other languages), consonants at the end of a syllable often become pretty voiceless (therefore the "t"-sound at the end sounds almost "hissed").
But as a native speaker I agree, in this example it sounds a bit weird and overdone.
Does this mean "We are constructing your bed" or "We are tidying your bed"? Or, as in English, could it mean either?