This is the 14654th most frequent German word.
moralische
"Relating to morals or ethics."
Here, 'moralische' is an adjective describing 'Integrität' (integrity), specifying the ethical aspect.
Seine moralische Integrität war unantastbar.
His moral integrity was unassailable.
In this sentence, 'moralische' describes 'Verantwortung' (responsibility), referring to a commitment based on ethics.
Wir haben eine moralische Verantwortung, der Wahrheit zu folgen.
We have a moral responsibility to follow the truth.
Here, 'moralisches' as an adjective modifies 'Dilemma,' relating it to ethical decision-making.