Is it worth losing a sale to keep a customer's trust?

You have already answered this in your gut, and your gut is right. A sale is one day's money. Trust is years of it, and something more: it is the reason you can look your customer, and yourself, in the eye. When you turn away business you could have taken by bending the truth, it can feel like loss. It is not. You are trading a small, quick gain for a name people rely on. That name is the most valuable thing you own, and it is built precisely in the moments you choose it over the easy dollar. So when the choice comes today, and it will, make it simple. Ask which one you can live with tomorrow. Then tell the truth, do the honest work, and let the trust compound. That is how a good reputation is actually made, one refused shortcut at a time.