So what?
Where do you get people who come onto your property to perform work at your private residence?
Are you not capable of asking them for business licenses, city licenses, professional references, or to see if they are insured and or bonded? Ya think typical illegal aliens are going to have these documents available to provide you?
Why are you evading these simple questions?
I believe E-Verify is only for employers who have set up corporate accounts (not generally for homeowners with household employees). And individual housekeepers likely won’t have business licenses or city licenses. A recommendation by a neighbor is how lots of people find housekeepers. So while you could ask if someone is here legally, it would be difficult to verify. And you still haven’t answered the question about if someone would need to be there every week verifying whether the different individual lawnmowers or other workers who show up are here legally.