What would "lernestrejo" be?
I think that would be the place (-ejo) for the leader/boss (-estr-) of learning (lern-), since the order of the affixes matter greatly in Esperanto. In other words, this doesn't really make sense.
Maybe the principal's office?
This might very well be true. I didn't think of that even though now it seems super obvious to me from my own description :D
That would presumably be lernejestrejo, rather than just lernestrejo, given that principal is lernejestro.
Work "at the school" is also perfectly correct English and a valid translation for this sentence.
Then you should probably report it
Mi preferas por traduki "lernejestro" tiel "schoolmaster". Mi pensas ke tio ŝajnas simila ol la nomo de MtG karto. (Aŭ ĉu oni dirus "MlR karto" -- Magio: la Renkonto"?)
Aktuale, ili laboras sur la ekranoj.
It is quite common, in the UK, to refer to the headmaster or headmistress as the head. That probably sounds weird to Americans.
TFW you put 'principle' instead of 'principal'.