The closest words that I found are "considerate" and "thoughtful"
For example, consider the following sentences.
He was very considerate about asking for a favor because he was already indebted to her.
He was very thoughtful about asking for a favor because he was already indebted to her.
These words are not exactly what I was looking for because of the following reasons.
- Both of these words are an action and not a feeling.
- "Considerate" is mostly used for the person who is on a higher ground.
However, these words somewhat serve the purpose.
There is a word for this in Urdu language called "Haya"
- "Haya", noun translates to "Modesty"
- "Haya Aana", verb translates to the positive shame that I was talking about. The person is already indebted and feels shame in inconveniencing the other person by asking for another favor.