Are there any reasons for a router to change the value of TCP-CHECKSUM?

I had a multiple choice question in a test that went like this:

Which of the following fields in the SYN packet(TCP) will NOT be modified by the router?

1. All of these fields will be modified by the router
2. Source MAC
3. IP TTL
4. TCP Checksum

Also, I know the following information about the router (it might not be relevant to this specific question cause there were more questions)

• IP address range 96.214.187.144/29
• router at IP address 96.214.187.151
• The router also serves as a DHCP server

I chose answer number 1: All of these fields will be modified by the router, but apparently the correct answer was TCP Checksum.

I want to know if I have something to "cling" to , to justify my answer. maybe a firewall could have change that? maybe nat? (cause that what I remembered when answering the question)