I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with.
DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed with the law firm of Natoli-Lapin, LLC on the basis of this posting.
I would need to understand more about your business before I could advise you about this.
Andrew M. Bonderud, Esq. -- Licensed in FL & TN; The Bonderud Law Firm ,P.A. Andrew's posting here is not to be considered legal advice nor does an attorney-client relationship exist.
If that Agreement forbids "scraping" then, no, you may not lawfully copy the information published on that website. Doing so would be, at least, a breach of contract and, perhaps, copyright infringement or even unfair competition.
Your own intellectual property attorney must evaluate your particular situation to assess the risk that your company is taking on by scraping such websites. Good luck.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
"all information is public" - not likely. More likely, all information is protected by copyright since copyright protection is automatic.
Some scraping is legal, some is not. You don't say what or how you scrape, so we can't say whether or when you're legal until Paul Harvey or you tells us "the other half of the story"
You need a lawyer's help not free advice here based on no or little facts.
"I am fiercely loyal to those willing to put their money where my mouth is."
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.