Checking if file exists before removing it in makefile

Honestly, that's an XY problem, it is not due neither to the fact that the project is a C++ one nor that it uses the spec C++11.

Because of that, the title of the question is a bit misleading, as well as its tags.

Anyway, you can use the option -f. From the man page of rm:

ignore nonexistent files and arguments, never prompt

So, it's enough to use the following line:

 rm -f charstack.h~ charstack.cpp~ main.cpp~ makefile~ error.h~ error.cpp~

Actually, it doesn't check if those files exist, but also it doesn't complain if they don't exist.

Even though this question has been answered, I attach a different solution that works for both files AND directories (because rm -rf DIRNAME is not silent anymore)

Here is a rule for removing a directory in variable ${OUTDIR} only if the directory exists. The example is easily adjusted for files:

clean:
    if [ -d "${OUTDIR}" ]; then \
        rm -r ${OUTDIR}; \
    fi \

Note that the key observation is that you have to write the usual bash if-then-esle as if it where on a single line (i.e. using \ before a newline, and with a ; after each command). The example can be easily adapted to different (non-bash) shells.