Does an indemnity compensation payment tax to be taxed again?

Daniel

Hi
A former employer of my client explained about her indemnity compensation on her final settlement figure as below:
As for indemnity figure of GBP 258,387.65 on the pay slip which includes company’s 50% share of tax of GBP 38,366.10 which is than grossed up by GBP 31,390.65 because this is paid employer and the total tax liability of the employer equates to GBP 69,756.75 which is added to actual indemnity of GBP 188,630.90 making total of gross indemnity of GBP 258,387.65 shown on the pay slip.
I am not sure that they did a right thing. Looks to me the £69756.75 is a tax that should not be taxed again!
Am I right? Please advise