Would the other person be waiting for some type of monetary retribution?

That's difficult to say, since the other person is unknown to you. It may very well be the other person is just acting out of kindness, and not expecting a reward at all.

If not, could I myself offer such reward? Would it not be considered rude?

I would say that yes, you can. Where I come from (The Netherlands), offering to reward a person who returns an expensive/important item is definitely not rude. It is seen as an additional expression of gratitude. But be prepared to graciously accept a stranger's kindness if they refuse your offer of money.

If your monetary reward is declined, just be sure to thank the other person very much, and show how glad you are that you have your phone back, and that you are even happier that the other person is so kind they feel that they do not need to receive a reward.

In my personal experience, when returning a jewelry item with lots of emotional value, the other person offered me a monetary reward as well. I politely declined, and then the other person managed to conjure up a thank-you card from somewhere. She had written some very kind words on it, and I must confess I am still keeping it today.

So I would say, definitely don't hesitate in offering a monetary reward, but don't push it if the other person declines. And a thank-you card is a very good back-up.

Would the other person be waiting for some type of monetary retribution?

That's difficult to say, since the other person is unknown to you. It may very well be the other person is just acting out of kindness, and not expecting a reward at all. On the other hand, you stated your concern about the stranger having made some costs by traveling to the public meeting place. This still does not mean the stranger is 'expecting' a reward, but it might be nice to offer one to him/her anyway.

If not, could I myself offer such reward? Would it not be considered rude?

I would say that yes, you can. Where I come from (The Netherlands), offering to reward a person who returns an expensive/important item is definitely not rude. It is seen as an additional expression of gratitude. But be prepared to graciously accept a stranger's kindness if they refuse your offer of money.

And in your case, you could say something like:

I'm really appreciating what you did for me, and I would like to at least reimburse you for some of the costs you might have made travelling to this place.

If your monetary reward is declined, just be sure to thank the other person very much, and show how glad you are that you have your phone back, and that you are even happier that the other person is so kind they feel that they do not need to receive a reward.

In my personal experience, when returning a jewelry item with lots of emotional value, the other person offered me a monetary reward as well. I politely declined, and then the other person managed to conjure up a thank-you card from somewhere. She had written some very kind words on it, and I must confess I am still keeping it today.

So I would say, definitely don't hesitate in offering a monetary reward, but don't push it if the other person declines. And a thank-you card is a very good back-up.

Would the other person be waiting for some type of monetary retribution?

That's difficult to say, since the other person is unknown to you. It may very well be the other person is just acting out of kindness.

If not, could I myself offer such reward? Would it not be considered rude?

I would say that yes, you can. Where I come from (The Netherlands), offering to reward a person who returns an expensive/important item is definitely not rude. It is seen as an additional expression of gratitude. But be prepared to graciously accept a stranger's kindness if they refuse your offer of money.

If your monetary reward is declined, just be sure to thank the other person very much, and show how glad you are that you have your phone back, and that you are even happier that the other person is so kind they feel that they do not need to receive a reward.

In my personal experience, when returning a jewelry item with lots of emotional value, the other person offered me a monetary reward as well. I politely declined, and then the other person managed to conjure up a thank-you card from somewhere. She had written some very kind words on it, and I must confess I am still keeping it today.

So I would say, definitely don't hesitate in offering a monetary reward, but don't push it if the other person declines. And a thank-you card is a very good back-up.

Would the other person be waiting for some type of monetary retribution?

That's difficult to say, since the other person is unknown to you. It may very well be the other person is just acting out of kindness, and not expecting a reward at all.

If not, could I myself offer such reward? Would it not be considered rude?

I would say that yes, you can. Where I come from (The Netherlands), offering to reward a person who returns an expensive/important item is definitely not rude. It is seen as an additional expression of gratitude. But be prepared to graciously accept a stranger's kindness if they refuse your offer of money.

If your monetary reward is declined, just be sure to thank the other person very much, and show how glad you are that you have your phone back, and that you are even happier that the other person is so kind they feel that they do not need to receive a reward.

In my personal experience, when returning a jewelry item with lots of emotional value, the other person offered me a monetary reward as well. I politely declined, and then the other person managed to conjure up a thank-you card from somewhere. She had written some very kind words on it, and I must confess I am still keeping it today.

So I would say, definitely don't hesitate in offering a monetary reward, but don't push it if the other person declines. And a thank-you card is a very good back-up.