Removal of a character to make a string a palindrome
Some Improvements:


Your checkPalindrome function is returning whether the string is a palindrome or not. What if it returns an index, at which it fails? 
Try working with that. Right now, you are calling the checkPalindrome function O(string-length), and checkPalindrome in itself is O(string-length), making it a square time algorithm.

Wikipedia article on Big O notation
A minor improvement: do you need to iterate over the entire string to determine if it is a palindrome?