my grandaughter

It's horrible to have a loved one steal from a loving parent or grandparent. You don't say what was stolen whether cash or say jewellery,
Is she a regular visitor and do you know if she ever stole from you, her parents or anyone else.
It sounds as though she was pleading poverty and you gave her some cash. One question, of course, is why is she so broke? Do you feel able to ask her.

You need to speak to her about it. Nobody should be stealing from anyone and to do it from family when they have given you money as well makes it even worse.

Yes, this is sad. You don´t mention what it is that she stole or what or your relationship with her is. Or, indeed, what her situation is. Is she a troubled young person? Does she visit regularly? Is the son who moved to the US her father and is she also on her own now? My mother used to claim that visitors stole things from her, but the "stolen" items were usually found later because she´d put them somewhere herself. It is quite a strong accusation to accuse someone of stealing. Perhaps, if you are absolutely sure, and you are close to her, you can text her, something along the lines that you noticed that she was not herself and would she like to drop by to talk about it? You say she is in trouble financially, she might have been hoping for more than £10 from her grandmother. It would be good to get this into the open and talk about it. And silly to fall out over it. You may well need her in years to come.

I am so sorry, you must be so disappointed. And clearly hurt.
Have you asked her about it, or will you not mention it and be sure it never happens again.
My heart goes out to you.