I might be embarrassed to use jQuery for a *simple landing page." Not because jQuery is dated, or I give a hoot about others' opinions, but 'cuz it's big...is the weight of jQuery justified? VanillaJS remains a viable option.
If the use of jQuery is reasonable, is it adequate? If it is reasonable AND adequate, is the landing page the front door to a site/app/platform that will use other, more heavy-weight libraries? Once you and your visitors pay the download cost for your choice of library the first time, it likely won't need to be paid again; if jQuery won't be used for the remainder of the app, then I would probably standardize the landing page to use the heavier-weight kit that will be common throughout the later parts.
Does your shop own a population of developers similarly well familiar with jQuery and your other library(ies) of choice, e.g., those favored by your CTO?
There's a network of interrelated issues to drive the decision as to which, if any, framework(s) to employ. I'm mostly concerned with performance, user experience, supportability, and cost-over-lifetime. I see the balancing of concerns such as bandwidth, shop standards, and developer skills as the measure by which to assess jQuery's appropriateness for use. The opinions of "other developers" as relates to the age of jQuery (or any tool extensively represented in my code-base) strike me as irrelevant.
Hammers come in different shapes and sizes for a reason. A hammer's age should rarely be the basis for choosing it.