As a first step, you can try gdbserver: Remote debugging using Eclipse CDT or The best variable that examines when debugging C ++ code with Eclipse / CDT or Eclipse cdt remote build and remote debugging on different servers offer tips on this.
Depending on your Linux distribution, the hudson server may be configured as computer B. Hudson support - Ubuntu, Debian, Oracle Enterprise Linux, RedHat, CentOS, Fedora, openSUSE as you can see here .
Hudson was developed in Java, but it is not an agnostic of the language, so it also works for C.
In general, you can commit your changes (from Comp A directly or to the central Git server), and Hudson (runs on Comp B) will create it and deliver it to your debug server (Comp C), on which you run GDB.
I do not have enough experience with CDT, so I can not give you more detailed instructions on how to configure all this, in addition to links to manuals. And you will need to check if GDB supports a Windows / Linux connection.
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