Always be tender when you're offering debt. If you say something like "take this loan, you filthy deadbeat putz," you're going to cause hurt feelings.
Besides good etiquette, the term "debt tender offer" has a specific financial meaning as well. It's a method by which a company buys back debt securities it has issued. In this way, the company reduces its debt load (See: Debt Load).
Think of it like paying back a loan, only instead of getting the loan from a bank or your Uncle Barry, you got it from thousands of anonymous investors.
Rather than tracking each of these people down individually, the company offers a tender offer. Which means it publicly announces that they will repurchase the securities at a certain price, with the transaction set to take place at a certain time. The firm then waits for the investors to contact them to take it up on the offer.
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