Given a string with parentheses, write a function that removes the minimum number of characters to balance the parentheses.

To remove the minimum number of parentheses to balance a string, you can use a stack-based approach. Iterate through the string, pushing the index of each opening parenthesis onto a stack. When you encounter a closing parenthesis, if the stack is not empty, pop an index (meaning a matching pair is found). If the stack is empty when a closing parenthesis is encountered, mark this closing parenthesis for removal. After the first pass, any indices remaining on the stack correspond to unmatched opening parentheses, so mark them for removal as well. Finally, construct the result string by excluding characters at the marked indices.