The short answer to this kind of question is no. Rebates, in general, are not taxable income to an individual taxpayer, unless that person first took a tax deduction for the cost of the item(s), when they originally bought the product(s).
That would be true, for instance, where a taxpayer has a business activity, and the rebates relate instead to an expense (i.e., tax deduction) for a good or service used in the conduct of that business.
In that instance, yes indeed -- a rebate on a purchased item or service does have a tax impact. However, if the item(s) are purely personal in nature, and with personal property specifically, the answer is no . . . for the reason that the underlying expense wasn't tax deductible in the first instance.
In other words, no deduction = no later need for a reversal (i.e., you don't need to report as taxable income) when a rebate is issued to you. It can safely be ignored, as the rebate is not considered taxable.