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you should claim on the warranty instead.
The fact that they are honoring their warranty by giving you a refurbished phone as a replacement, isn't an issue. Its their choice and is industry standard, thats the way warranties work. The fact that you are expecting them to pay you for them honoring the warranty is absurd.
Unless you had one that specified new for old...
https://support.google.com/store/answer/7540759?hl=en&ref_topic=7544605
EXCLUSIVE REMEDY: If a defect arises and you return your Phone during the Limited Warranty period (which is two years for new devices and ninety days for refurbished devices), Google will in its sole discretion and to the extent permitted by law either repair your Phone using new or refurbished parts, replace your Phone with a new or refurbished Phone functionally at least equivalent to yours, or accept the return of the Phone in exchange for a refund of the purchase price you paid for the Phone. If Google repairs or replaces the Phone, the repaired or replaced Phone will continue to be warranted for the remaining time of the original warranty period. All returned parts for which you have received a replacement will become the property of Google. Nothing in this Limited Warranty will reduce or otherwise affect your statutory rights in relation to the Phone.
To make a claim under the Limited Warranty, go to g.co/pixelcare. We’ll need your name, contact information and the IMEI or serial number for your phone (located at Settings > System > About Phone > Status). You will need to provide a purchase receipt.