An unremovable (but replaceable) search domain is usually passed along by the router from the ISP/modem, if separate .
Here on Sierra, at least, and I'm sure earlier versions too, tcpdump is included with macOS.
You'll need to use Terminal, and your admin password, and copy/paste a command, then either renew DHCP or power off/on wifi.
sudo tcpdump -i en0 -vv | grep Domain-Name
copy the entire text above, then paste it into Terminal, while using your Mac in an admin user account
press enter/return : you'll be prompted for your admin password. Type it in, followed by enter/return; it won't be echoed on the screen. You can expect an initial output similar to below
tcpdump: listening on en0, link-type EN10MB (Ethernet)
Now power wifi off/on or renew DHCP lease & here, anyway, I see this after a few seconds :
Subnet-Mask, Classless-Static-Route, Default-Gateway, Domain-Name-Server
Domain-Name, Option 119, Option 252, LDAP
Subnet-Mask, Classless-Static-Route, Default-Gateway, Domain-Name-Server
Domain-Name, Option 119, Option 252, LDAP
Domain-Name-Server Option 6, length 4: 10.0.1.1
Domain-Name Option 15, length 20: "hsd1.nh.comcast.net."
After say 10 seconds, or if you see a similar output; quit tcpdump in Terminal by using ctrl c
Here anyway, the relevant line is 'Domain-Name Option 15' but it should be obvious because your search domain ought to be there, in quotes.
Mine's forced by the ISP via a cable modem, then AirPort Extreme. No menus to clear/alter it that I have ever seen.