This is exactly why I contribute tens of thousands of lines to F/OSS projects.
Your mettle has never truly been tested until you have hundreds of developers, from around the world, pointing out your idiocy in an excruciatingly specific manner. After your ego has been throughly decimated, then you can improve.
This is closer to how I would do it in practice.
void condense_by_removing (char *z_terminated, char char_to_remove)
{
char *next = z_terminated;
while (1) {
while (*z_terminated == char_to_remove) ++z_terminated;
if (!(*next++ = *z_terminated++) ) break;
}
}