Pip award

I have been awarded pip enhanced care and enhanced mobility. My dla mobility ends on 25th Dec and pip both rates begins on 17 Jan.
While on dla I did not receive care component only mobility. Therefore should the pip care rate be backdated to the date on pip application form? I called up dwp and they told me the decision is no and I can them to reconsider this. Should I ask for reconsideration or leave it? I'm afraid it may affect my award