You could then give them a 3 day notice to cure/comply or quit (or however it's done in New Jersey), meaning pay the water bill in the next three days or move, because you're in breach of contract.

Then explain you saw the 2nd dog and will be expecting the additional deposit for the dog ASAP.Thank them for complying and don't bother checking if the 6th guy ever leaves or not.Tell them they will be receiving some paperwork in the mail stating what your concerns are just to keep everything on a professional level, but you'd rather work it out with them because they've been good tenants.If these guys are paying on time and not giving you trouble other than this, why not approach them with a lease extension instead of looking to take additional funds out of the security deposit and winding up with an empty rental?

Do you think that if I went to the tenant with something in writing as well and a friendly conversation, the risk of her losing her voucher for herself and her two kids would be enough to comply? 

Application Process & Screening Criteria:Liberty Management, Inc. is committed to equal housing and we fully comply with the Federal Fair Housing Act (FFHA) and the Fair Credit Reporting Act (FCRA).

Did this incident affect their ability to comply with the terms of the rental agreement?

Normally I could get a tenant to comply. 

I would serve her a Notice to Comply, which states she needs to clean it up, and be as specific as you can possibly be.

File a small claims lawsuit since they did not comply with the deadline.

Granted, they'd probably be stretching the truth on that, but they might win.So, what I would do, is give them a 3 day notice to comply or quit (or whatever the law states where your rental is), regarding allowing the contractor in. 

It complies with state law and gives you the right to enter the property with no notice.That's not just a nit to pick - when you get involved in an argument with a tenant, it's important that you not confuse issues with all sorts of extraneous things.