Received legal notice from a company

1) On 19th April 2022, I received an offer letter + employment terms & conditions document (annexure) from a payroll company (payroll company in Bangalore, work location client company in Pune). I accepted the offer on mail, joining date was agreed as 1 June 2022, however I did not send signed, scanned copies of both documents to employer as it was not asked by them at that time. 2) On 30 May, company asked me the documents (salary slips, marksheets, aadhar card etc. ) Which I sent to them via email. 3) On 31 May, they sent me an appointment letter, NDA & same annexure and asked me to reply with signed scanned copies. I did not sign & send these documents that day as it was late night. 4) Next day on 1st June, I went to the client company. No formalities were done at client company, I came to know how bad this client company is. In the afternoon, I received another offer and the same day evening, I wrote a mail to payroll company that I won't be working with you. 5) The payroll company has sent me a legal notice saying, since I did not serve the notice period, I must pay certain amount (as mentioned in offer letter annexure), otherwise they will go to the court. Do you think their notice will stand in court? Please help me...need an expert advice. Thanks