Proxy lists grade proxies by what they add to plain HTTP requests. A transparent proxy passes your IP along in X-Forwarded-For. An anonymous proxy hides your IP but adds a Via header or similar. An elite proxy adds nothing: the request arrives looking as if the proxy's IP sent it directly.
Check it yourself
Send a plain HTTP request through the proxy to a header echo and look for Via, X-Forwarded-For, Forwarded or Proxy-Connection in the reply:
curl -s -x http://USERNAME:PASSWORD@HOST:PORT http://httpbin.org/headers
None of those headers should appear. Use an http:// target for the test: HTTPS requests travel inside an encrypted tunnel the proxy cannot modify, so any proxy passes over HTTPS.
What elite does not buy you
"Elite" describes headers, and headers are only one of the signals a site reads. A request from an elite proxy on a hosting network is still identifiable by its ASN, still carries the IP's reputation, and still shows your client's TLS fingerprint. Commercial proxies are normally elite as a matter of course, so the label is not a reason to choose one vendor over another.
Common confusion
Free proxy lists stamp "elite" on entries based on a check that may be days old, and many of those proxies are misconfigured or compromised machines. The label says nothing about who runs the proxy or what it logs. Free proxies explains what can go wrong and how to test one safely.