Absolutely you need to examine the terms of the warranty. On one of Judge Judy's new streaming shows she had a case where someone had purchased a used BMW from Carmax for $30,000 (first mistake!) and another $2,500 for extended warranty (oops!). When his engine blew up he was denied coverage due to conditions in the fine print.

You better read every word of it and see if it's actually worth the cost.  Usually, the dealer finds a way to get out of them, by telling you "That's normal," or "We couldn't hear anything."  I don't think they are worth the paper they're printed on most of the time.

If you really are intent on keeping the truck a really really long time, you may want to consider it BUT find out what company is the provider and of course the terms (length of time and mileage). When I bought my wifes certified used Honda CRV in 2012 he offered me the "Honda" extended warranty. First thing I said was "Hey, its a Honda! Why the heck would I need extra warranty". So with that, he cut the price of the warranty from $1600 to $1000 and ya know what, I said why not as I will be keeping the car long term. Well, 6 years later and 108k mile on the CRV, the dam A/C system went. My Honda warranty was 10 years/120k miles. Took it into Honda, no fuss no muss and the $1400 bill for the system replacement was covered 100%. Nothing is perfect, not even Hondas or Toyotas so its all a gamble/risk. If you can get a smoking price deal on it and its a true Toyota extended warranty, not that Carshield crap, you may want to strongly consider it, again if your planning to keep your Tundra for 10+ years. Just my experience.