It is okay to bleed red ink all over their contracts before sending it back to them. I do that with almost every one. You've got to protect yourself and if their contracts are so one-sided that they put all of the liability on you, fix it before sending the signed contract back!
Then, if it's a company that requires you to sign every single PO they send to you, save a copy of the marked up contract in a file so you can send it back (with a new signature and date) with the new PO they send you just to make sure they didn't add anything funny to it. That sure beats having to re-read every single contract every single time you get a little service job!
Just because they send it to you that way doesn't mean you have to accept it. It's a contract and you need to make sure it is a fair deal for both parties.
That includes their, usually ridiculous, "budget" amounts. Those crazy-low numbers are just a negotiation ploy designed to get you to work for pennies. That doesn't mean you have to accept it if you want the work. Change it to what the job is actually worth and send it back. You'll usually get it ... if you're a good company that they want to work with.