Is Content-Transfer-Encoding an HTTP header?

According to RFC 1341 (made obsolete by RFC 2045):

A Content-Transfer-Encoding header field, which can be used to specify an auxiliary encoding that was applied to the data in order to allow it to pass through mail transport mechanisms which may have data or character set limitations.

and later:

Many Content-Types which could usefully be transported via email are represented, in their "natural" format, as 8-bit character or binary data. Such data cannot be transmitted over some transport protocols. For example, RFC 821 restricts mail messages to 7-bit US-ASCII data with 1000 character lines.

It is necessary, therefore, to define a standard mechanism for re-encoding such data into a 7-bit short-line format. (...) The Content-Transfer-Encoding field is used to indicate the type of transformation that has been used in order to represent the body in an acceptable manner for transport.

Since you have a webservice, which has nothing in common with emails, you shouldn't use this header.

You can use Content-Encoding header which indicates that transferred data has been compressed (gzip value).

I think that in your case

Content-Type: application/pdf

is enough. Additionally, you can set Content-Length header, but in my opinion, if you are building webservice (it's not http server / proxy server) Content-Type is enough. Please bear in mind that some specific headers (e.g. Transfer-Encoding) if not used appropriately, may cause unexpected communication issues, so if you are not 100% sure about usage of some header - if you really need it or not - just don't use it.

Notes in rfc2616 section 14.15 are explicit: https://www.w3.org/Protocols/rfc2616/rfc2616-sec14.html

"Note: while the definition of Content-MD5 is exactly the same for HTTP as in RFC 1864 for MIME entity-bodies, there are several ways in which the application of Content-MD5 to HTTP entity-bodies differs from its application to MIME entity-bodies. One is that HTTP, unlike MIME, does not use Content-Transfer-Encoding, and does use Transfer-Encoding and Content-Encoding. Another is that HTTP more frequently uses binary content types than MIME, so it is worth noting that, in such cases, the byte order used to compute the digest is the transmission byte order defined for the type. Lastly, HTTP allows transmission of text types with any of several line break conventions and not just the canonical form using CRLF."