Target's standard return window is 90 days, and you're well within it at three weeks. Since you paid with a card (which is how most people shop these days), they absolutely can pull up your purchase without needing the physical receipt - their system ties transactions to payment methods instantly. Even if you used a debit card, a credit card, or their RedCard, you're golden.
The catch everyone mentions is cash purchases, but here's a practical workaround they don't talk about: if you do have your card or ID on you, bring both. Target employees can sometimes manually verify purchases faster if they have multiple data points. And if you bought it in-store at a specific location, returning it to that same store makes the lookup even smoother since their inventory system will have the record. If you paid cash and somehow have the email confirmation or your bank statement showing the charge, bring those too - it all helps.
One more thing: that grinding noise in the motor sounds like it could be a defect rather than user error, which actually works in your favor. Target's pretty reasonable about warranty issues and mechanical failures even without a receipt. Bring the blender, explain what happened, and don't overthink it. The whole thing should take ten minutes.