In Framework 4.7.1 there have been some GC improvements.
https://learn.microsoft.com/en-us/dotnet/framework/whats-new/
I am currently running a service that was built under 4.6.1.
If I install 4.7.1 on my server without re-compiling my program under 4.7.1 and referencing it will the new GC improvements apply or do i have to recompile?
Yes, they will.
If you install .NET Framework 4.7.1 on the machine, even if the application targets .NET Framework 4.6.1 it will still run on the 4.7.1 Framework since the .NET Framework 4.7.1 install is an in-place update.