ESA/private pension

I am in receipt of contributory based ESA and I receive a private pension.
After several attempts trying to ring the dwp to inform them of an increase in my private pension, I wrote telling them.
I have received a letter from them today claiming that I failed to inform them.
They were aware of the increase in my private pension even before I was informed by my pension provider and the dwp wrote to me telling me what my new private pension amount would be.
I am wandering whether I should respond to their letter explaining that I tried ringing them several times before writing to inform them.
Your advice would be appreciated.