Why "fi l-bayt" and not "fil bayt"?
The English transcription is not standardized. One could write "fi l-bayt" or "fil bayt" or "fi-l-bayt", doesn't matter, it all reads the same way.
Sorry I formulated my question a little bad. What I'm wondering about is the choice of mark over the alif in "l-bayt". Why do they use this mark that was newly introduced, instead of no mark like in most sentences earlier in the course?
The mark means precisely that the alif is not pronounced. Normally (e.g. in the beginning of a sentence) it would be al-bayt, but the preceding vowel eats the "a" sound.