To me -- unless you have hundreds or even thousands of pages -- on-site search just means there's something wrong with your site. Admittedly, you have a very active blog, or a ultra-active forums, THEN it's neccessary -- but at that point whatever CMS you are based on should already have that -- and if what's built in isn't good enough, you should be tying into a low level library like Sphinx, instead of a third party system.
Looked up this "denote.io" thing, and their site reeks of feel-good marketspeak -- with loaded words, card stacking and glittering generalities; the implementation seems too complex for it's own good, and just strikes me as attempting to offload on a third party something 90%+ of websites shouldn't be wasting time doing in the first place.
Admittedly, seven or eight years ago I was trying to do the same thing -- but I got a wake-up call; it led to a total distrust of things like this because if the front end code of things like this are such a needlessly complex mess, how can I possibly trust their back-end code?
A "view source" of the home page of their website should be enough to scare you away from using it.