B. is saying that the minimum they can do, (as Pip says) to pay back the debt - in this case to compensate for the spilling of the coffee - is to replace the coffee by buying a new one. Probably they feel so guilty that they might also have considered paying for the cleaning of the shirt...

‘To owe’ means that you must pay back a debt of some kind. For example, I paid for your first drink and now you owe me a drink.

In this sentence, "I owe you at least" means: * "I feel obligated to repay you in some way, even if it's something small."
The speaker feels responsible or guilty for spilling coffee and wants to make up for it by buying a coffee or doing something to apologize. Example Explanation: * "I owe you at least a coffee" implies:
"I made a mistake, so the least I can do to make up for it is to buy you a coffee." It reflects politeness and a desire to fix the situation.