Final answer:
The explicit resolution to Teruo's issue with worrying about reputation is not provided, and it would typically involve balancing or prioritizing conflicting duties ethically.
Step-by-step explanation:
The resolution of Teruo's issue regarding his reputation and the integrity of his word, based on the context provided, is not explicitly listed among the options given. However, when dealing with conflicts between conflicting duties such as honesty and non-maleficence (avoiding harm), one ethical approach could be to seek a balance or prioritize based on potential outcomes. In the case of an associate professor spreading rumors due to tenure concerns, the problem might be addressed either by confronting the individuals involved or through institutional channels that handle professional misconduct.