Dad says the oak is fine. The estimate is under the magnet on the fridge, the crew says Thursday works, and everybody wants the limb over the garage gone before the next storm. Before a saw starts, the paper decides who pays if a limb lands on the roof, who hauls the wood, and what the crew owes if the driveway gets torn up. Read the paper first.
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Check the crew's insurance before the crew arrives
Ask for a certificate of insurance and read three things on it. The company name must match the name on the estimate exactly. It should show general liability coverage and workers' compensation, or a written statement of why workers' comp does not apply. The certificate holder line should name Dad, or the property owner, so the insurer notifies the right person if the policy changes.
Then call the insurer listed on the certificate and ask whether the policy is active and whether the dates cover the job. A certificate can be out of date or issued for a different company. The phone call takes ten minutes and settles the question.
Write the scope line by line
"Remove tree" is not a scope. Write what the crew will do: fell the tree or the named limb, cut the trunk into pieces of a stated length, remove the stump or grind it to a stated depth, and clean the work area. Each item either appears on the quote or it does not. If the quote says nothing about stump grinding, assume it is not included until the crew writes it in.
Look for the exclusions. Fence repair, sprinkler lines, landscape beds, gutters, and utility line work are common exclusions. An exclusion is not a problem if you know it is there. The problem is finding it after the crew has left.
Read the debris clause
Debris is where most tree jobs go sideways. Write down who hauls the wood, where it goes, whether the chips are left on site or removed, and whether the crew rakes up sawdust and small branches. If the quote says "debris removed" with no further detail, ask what that means in writing. A short sentence in the contract fixes the answer before the trucks come.
Find the damage clause
Ask what happens if the crew damages the house, a car, a neighbor's fence, or a buried line. Look for language that says the crew is responsible for damage caused by its own negligence, and check whether the certificate's liability limits fit the size of the risk. If the estimate says nothing about damage, put the question to the company in writing and keep the answer.
Check the street, the lines, and the permit
If the tree sits near a street, a sidewalk, or overhead wires, stop and ask who handles the utility side. Utility companies control their lines. The crew should not touch a line, and the contract should say so. Ask the company whether a permit is needed for this job. The city permit office for your address answers that question, not the crew, and you can find the right office through the directory on Local Help in St. Louis.
Compare the quotes on the same lines
Get at least two or three written quotes built on the same scope. Compare them line by line, not by total. One quote that includes stump grinding and haul-away may cost more than another that leaves the stump and the brush on the lawn, and the difference is the work you actually need.
Watch the payment terms too. A reasonable deposit, payment on completion, and any change to the scope written as a signed change order are the usual shape. Be wary of cash-only requests or payment in full before work starts.
Confirm who signs
The person who signs the contract must have authority to sign for the house. If Dad owns the property and can sign, he signs. If someone else is signing for him, stop and confirm that person's authority before the crew gets a deposit. That is a question for the paperwork you already hold, not for the crew.
Your next move tonight
Call the insurer on the certificate and confirm the policy is active. Write the scope in a short list, with the stump, the debris, the exclusions, and the damage clause on separate lines. Email the list to the company and ask for a revised quote built on it. Keep Dad off the ladder and out of the yard while the crew works. The crew does the climbing, and the paper does the protecting.
This is paperwork guidance, not legal advice. If the damage terms or liability limits look large relative to the house, have someone who reads contracts for a living review them before you sign.