Vendor performed work I didn't authorize, what to do?

[Chad Green]

TL;DR is at the end of this post.

My tenant was having issues with the AC.  I told him to contact an HVAC company I had researched on a prior occasion.  I had previously scheduled for this same company to check on an AC at a different property, but the tenant never scheduled it.  This company had my contact info.  The exact wording in my email to my tenant:

"If you're unable to get it down to a more comfortable temp, I'll be happy to have someone come out to take a look at it, in which case I'd ask that you please try contacting [HVAC repair person] from [name of HVAC company]: [phone #]."

Tenant replied: "[HVAC repair person] is going to come out and take a look today so I'll keep you posted and have him give you a call if he expects to do anything that might cost more."

Next thing I know I get a call from the repair person saying he's got the AC system running cool again.  Said the main cause of the issue was a clogged up air filter (I know, my bad for not reminding my tenant about the importance of regularly changing filters (it's written in the lease that he must replace them every 3 months and that I'm not responsible for bills resulting in replacing filters)).  Coils were frozen so he had to defrost the coils.  That's understandable.  Then he said he took the liberty of also doing some "preventative maintenance"  Uh oh.  He said he would email me the bill.  So here's the bill:

1 Service call (July Special) 1.00 $100.00 $30.00
(30.00%)
No Tax $70.00
2 Labor (defrost and clean condenser coil) 2.00 $100.00 $20.00
(10.00%)
No Tax $180.00
3 Co2 Coil Cleaning 1.00 $25.00 $1.25
(5.00%)
$1.43
(6%)
$25.18
4 R-410a Refrigerant 2.00 $65.00 $0.00 $7.80
(6%)
$137.80
Subtotal (without tax) $403.75
Taxes $9.23
Grand Total ($) $412.98

As an aside, the fact that vendor added refrigerant is a red flag to me, as it's my understanding that cooling systems generally don't lose refrigerant unless there's a leak, in which case the leak needs to be addressed.

TL;DR: AC not cooling. I told tenant to contact vendor. Tenant said ok, said he'd have the vendor give me a call if he expects to do anything that "costs more." I don't hear anything until the vendor is done with the job, at which point the vendor calls me to say that the air filter was clogged, that the coils had been frozen over and so he defrosted them, and that he did some "preventative maintenance." He then sends me a bill for $412.98.

How do you all advise I handle this? Let him know that I didn't authorize the work and so offer to just pay him his service call fee? And if anyone knows anything about AC systems, do you think it's appropriate to charge $180 to defrost the condenser coil?