Cookieless is a marketing word doing several jobs at once. It can mean a tool that writes nothing to the device, a tool that writes something that is not technically a cookie, or an advertising approach that identifies people without third party cookies. Only the first of those removes anything from your banner, and it is the least common of the three.
The three meanings, and only one helps
A genuinely cookieless analytics tool stores nothing on the device and derives its counts from the request itself. A tool that has moved from cookies to local storage or a fingerprint has changed the mechanism and not the obligation, because the European rule covers storing or accessing information on terminal equipment rather than cookies specifically. And cookieless advertising usually means identity resolution by other means, which is more data about the person rather than less.
How to tell which one you bought
Open the site in a clean profile, load a page, and look at all client storage rather than only the cookie jar: cookies, local storage, session storage and indexed databases. If the tool writes anything persistent that identifies the browser across visits, it is in scope whatever the label says. This takes about two minutes and settles an argument that otherwise runs on vendor documentation.
What it is worth doing anyway
Removing a category from the banner is genuinely valuable: fewer decisions for the visitor, less to disclose, less to keep accurate when the site changes. If a cookieless tool answers the questions you actually ask of your analytics, swapping is usually cheaper than maintaining the consent plumbing around the tool you have. Just verify the claim yourself rather than taking it from the pricing page.
Questions people ask about cookieless
Is cookieless the same as consent-free?
No. The obligation follows storage and access on the device generally, not the word cookie. A tool is consent-free only if it stores nothing.
Does local storage need consent?
In the EU, yes, on the same basis as a cookie. The rule is about the visitor's terminal equipment.
Is fingerprinting a way around this?
It is treated as accessing information on the device, and it is more intrusive rather than less. Regulators have been explicit about it.
Will removing cookies fix my analytics accuracy?
It may improve consistency, because nothing is being blocked or expired. It will not recover the visitors who declined to be measured, if you are still asking.