The child benefit tax charge has been in place since January 2013 and affects anybody who claims child benefit and has an income of over £50,000. It still surprises me that many don't know about it from talking to friends and acquaintances if from no other source such as the Marin Lewis website and Mumsnet etc. It is unfair how it works but I don't make the rules so there is no point in pursuing that though I understand your frustration. You cannot have the tax charge cancelled.
The excess child benefit is clawed back by HMRC through the tax system and the amount that has to be paid back is dependent on the level of your income between £50,000 and £60,000. If you have an income of £60,000 or more, you will pay back all the child benefit. Take a look here and here for more information. There is a calculator behind the second link.
If you owe tax for 2018/19, provided you complete and submit a tax return to HMRC by 30 December 2019 you can choose to pay it back through your tax code over 12 months from April 2020. The tax owing for 2019/20 won't be payable until 31 January 2021 unless you choose to have that collected through your tax code over 12 months from April 2021. HMRC may alter your current tax code to claw back the excess child benefit being paid to you now.
Finally, your tax code is your responsibility, not HMRC's . That code determines how much tax you pay each month so it should be checked. HMRC are advised in arrears of child benefit payments.
I hope this helps but let me know if you have any further questions.