Since you mentioned 'bad backlinks', I'm going to assume it's a penguin penalty. Follow thise guide if you want to help your site recover from a penguin penalty: Penguin 3.0: The Definitive Guide To Diagnosis And Recovery - Forbes

Hi,

I had also a client that got google penalty. This link had give me some good advice.

Ultimate Guide to Google Penalty Removal - Moz

Hope that can help you too

Since everyone else who responded dropped a link I guess I'll do the same. Here is another good guide to help : 10 Steps to Remove Unnatural Link Penalties from Google

May a higher power have mercy on your clients business.

[DELETED]

you need to contact site webmasters to remove your site links.

First, get into their Webmasters Tools. See if/what messages they have in there. Download a backlink report from ahrefs, and start going through the links. Mark all the spam ones for later.

Once that's done, ideally you'd email webmasters before disavowing links, but most people skip that step and go straight to disavowing the links.

Then, submit a reconsideration request. Don't mention you're an SEO agency, just say you're the IT guy helping out.

You'll go back and forth with them 3-4 times, but eventually they'll lift the penalty (if it was a manual one to begin with).