Questions & Answers about Я хотел бы вернуть эту вещь.
Why is хотел in the past tense if I'm asking for something right now?
To say "I would like" politely in Russian, we use the conditional mood. You form this by taking the past tense of the verb (like хотел) and adding the particle бы. Even though it uses a past tense form, combining it with бы makes it a polite present or future request, just like "would like" in English.
How would a female speaker say this?
A woman would say Я хотела бы вернуть эту вещь. Because the conditional mood uses the past tense form of the verb, it must agree with the gender of the speaker (хотел for masculine, хотела for feminine).
What case is эту вещь, and why doesn't the word вещь change its ending?
It is in the Accusative case because it is the direct object being returned. вещь is a feminine noun that ends in a soft sign (-ь). For this specific group of feminine nouns, the Accusative form is exactly the same as the Nominative (dictionary) form, so it doesn't change. However, you can tell it's Accusative because the word for "this" changes from эта to эту.
Why do we use the perfective verb вернуть here?
When you say you want to return an item, you are talking about a single, one-time action that you want to complete to get a result. That requires the perfective verb вернуть. Its imperfective pair, возвращать, would sound like you want to return items repeatedly or as an ongoing process.