I only see "Quartal" being used for "the quarter of a year". Never seen it in a different context and I also only use it in this context. (I am a german native speaker). I guess this "im neuen Licht sehen" part is what made you think Quartal is for something abstract? It basically means that you look back at the last Quartal and now see aspects that you haven't seen before (e.g. it wasn't as bad as you thought it was). Hope that helps.
A season is a quarter of a year too but when you speak about "Quartal" you don't mean a season. The first "Quartal' for ex. is January, February and March (the first three months of the year) but a season is three different months for ex. winter is December, January and February. So a new "Quartal" starts is a new year but not a season.
At least in American English, I only see trimester used (perhaps inappropriately) to refer to divisions into three parts. For example, each academic "trimester" would cover roughly four months (including breaks), typically September--December, January--April and May--August. This usage does conflict somewhat with the "three-months" Latin etymology mentioned by Wikipedia. I suspect it developed as a bastardization of semester ("six-months" in Latin, but commonly interpreted as division into two parts), perhaps influenced by the division of pregnancy into three trimesters.
Anyway, if "trimester" and "quarter" are synonymous in Britain, Ireland, Australia, etc., then I would suggest reporting it as an alternative that should be accepted.
Is it completely inconceivable that Quartal could mean season? I think there is a little bit of an overlap between season and quarter in english in the way a season can just be a time span in the year (holiday season, hunting season) as can a quarter in terms of a financial year, the Tax year doesn't start from January everywhere in the world.
Just in case (as it was explained before in this thread): According to Google Dictionary, a quarter is a period of three months regarded as one fourth of a year, used especially in reference to financial transactions such as the payment of bills or a company's earnings. In German, Quartal [n] has the same meaning.