Does ICMP packet contain TCP header

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Generally: ICMP acts on top of IP, so ICMP packets don't contain their own(!) TCP header.

BUT the question is tricky in a sense that ICMP packets of some types (those ones reporting different problems, like in your trace - TTL exceeded, Destination unreachable etc.) according to RFC792 must contain some chunk of ORIGINAL datagram causing a problem.

In this case if original datagram used TCP, its TCP header will be present ICMP packet. It is not used for transport purposes though, but only for diagnostics purposes.