Is this the right use of "ensure"?

Most users (in the US) and most dictionaries would select ensure as the logical choice

make certain that (something) shall occur or be the case

However, insure would not be wrong

often followed by against to guarantee or protect (against risk, loss, etc)

we insured against disappointment by making an early reservation

often followed by against to issue (a person) with an insurance policy or take out an insurance policy (on)

his house was heavily insured against fire

after all his car accidents the company refuses to insure him again

The cited text refers to a warranty that the company is extending. The company is committing financial resources to make you whole if the product fails, something tantamount to an insurance policy.

Assure seems less apt. Most definitions and usage have to do with telling rather than effecting

to cause to feel sure or certain; convince: to assure a person of one's love

to promise; guarantee: he assured us that he would come

to state positively or with assurance

to make (an event) certain; ensure

(mainly British) to insure against loss, esp of life

All said, there is a justification for each in US usage.

Insure is related to business practices, like insurance. Assure is promising something to remove doubt ("I assure you that I will be home on time.") and ensure is guaranteeing a condition ("The airbags and other safety features ensure that you will be safe.")

In this case, I think that it could be changed to "assuring you have your peace of mind" to make it clearer, but in the current context I would agree that ensure would be correct because you are guaranteed peace of mind. Maybe your company means "insuring" literally though since the topic is a warranty.