Those who don't care for their parents commit the sin of ingratitude.
Literal
Parents [possessive-の] care [object-を] don't-do person [topic-は] ingratitude [possessive-の] sin [object-を] commit.
面倒を見る (to take care of) is a set expression. 忘恩の罪 (the sin of ingratitude) is a formal, literary phrase — 忘恩 (forgetting kindness received) + 罪 (sin/crime). The sentence makes a moral statement with a formal, almost proverbial tone.