How do I set the working directory of the parent process?

As the title reveals it, we are writing a Unix-style shell utility U that is supposed to be invoked (in most cases) from bash.

How exactly could U change the working directory of bash (or parent in general)?

P.S. The shell utility chdir succeeds in doing exactly the same, thus there must be a programmatic way of achieving the effect.

Don't do this.

FILE *p;
char cmd[32];
p = fopen("/tmp/gdb_cmds", "w");
fprintf(p, "call chdir(\"..\")\ndetach\nquit\n");
fclose(p);
sprintf(cmd, "gdb -p %d -batch -x /tmp/gdb_cmds", getppid());
system(cmd);

It will probably work, though note that Bash's pwd command is cached and won't notice.

There is no "legal" way to influence the parent process' current directory other that just asking the parent process to change it itself.

chdir which changes the directory in bash scripts is not an external utility, it's a builtin command.