A lost umbrella can be replaceable while the kindness that lent it is not.

Two different things can be lost at once, and only one of them costs money. The umbrella is a few pounds; what cannot be bought again is the fact that somebody noticed you were getting wet and handed you theirs without thinking about it. When you feel disproportionately bad about losing a borrowed thing, that is usually what the feeling is actually about.

Replace the object without ceremony and then tell the person what the gesture meant, which is the part they will care about. And where you are the lender, make it easy for someone to lose it.