## [Wolfram Language (Mathematica)], <s>53</s> 51 bytes

Byte count assumes CP-1252 encoding.

 ±{a___,Shortest@b___,c___}/;PalindromeQ[a<>c]:={b}

[Try it online!][TIO-j9quetfm]

[Wolfram Language (Mathematica)]: https://www.wolfram.com/wolframscript/
[TIO-j9quetfm]: https://tio.run/##NYxNCoMwFIT3niK4LIJW@2N/EQpdFEWLSxF5iUEDGiHGhYiH6hV6MWuKbh7zzbyZGmRJa5CMwDR9PwNkWWbEZSMkbaWHFZH5jOYlgorxXDQ1fSdwvZP0fBvwOEWCcYm8DYrlrIpXw7iiqOragPGuVfAoQQCRVLTI9NCgIaS7lmU7jmW5uoEUzzklIJ5h6C8OYJLTnGBYmBei91HQi4IvztZ2dvvD0T3pxr@gGhjW/yRJ03VK18bpBw "Wolfram Language (Mathematica) – Try It Online"

Defines a unary operator `±` (or a function `PlusMinus`). Input and output are lists of characters. The test suite does the conversion from and to actual strings for convenience.