neglect of social obligations; dishonorable conduct
Refers to failing to fulfill expected social duties, such as not returning favors, not attending important events, or acting ungratefully. Often implies a breach of 義理 (social/moral obligation).
お世話になった人に挨拶もせずに引っ越すのは不義理だ。
Moving away without even greeting the people who helped you is a neglect of social obligations.
failure to repay a debt
Specifically refers to not repaying borrowed money or a financial obligation, seen as a serious breach of trust.
借金を返さないのは不義理だ。
Not repaying a debt is a failure to meet one's obligations.
彼は不義理な態度で周囲の信頼を失った。
He lost the trust of those around him through his dishonorable attitude.
不義理 refers more broadly to failing in one's social or financial obligations, whereas 恩知らず specifically targets someone who ignores a debt of gratitude.
Compound of 不 (fu-, 'not') + 義理 (giri, 'social obligation, duty'). The reading ふぎり is a standard on'yomi combination.