void condense_by_removing(char* s, char c)
  {
    char* d = s;
    while (*d = *s++)
      d += *d != c;
  }

It always does the copy, then evaluates *d!=c. If what it just copied is equal to the forbidden character this evaluates as false, which in C is 0, and hence d is left unchanged.

If what it copied is not equal then this evaluates as true, which is 1, and hence d is incremented.