Agree that “biweekly” can mean every other week or twice a week. Maybe the lawn service meant twice a week, but the people reading the flyer saw it as every other week.
I personally tend to stick with the original latin meanings: bi = two, semi = half. Which would stipulate that biweekly means every other week (or every two weeks) and semiweekly would mean twice a week (or two times a week).
That said, I think the better way, given the rapid digression towards ambiguous language these days, would be to simply use one of the following phrases: "weekly", "every two weeks", "twice a week", "every other week", or "two times weekly". I remember reading something from another landscape company where the fella was adamant that you should not use these terms but instead use something like "7-day mowing plan" or "14-day mowing plan" or some other such nonsense, but I don't remember his rationale behind that.
Getting to the point of the OP - if this "new guy" really is offering bi-weekly for $35 per service visit, there isn't anything that can be done about it except replace the "customer" with a higher value "client". This guy is obviously not making it as a "handyman" (and probably for good reason), so I wouldn't expect him to make it in the "lawn care" business either - they are both service businesses after all, and as we all know, there is more to it than just cutting grass. Regardless of his skill as a handyman, I would contemplate that business is failing because he is one of those people that simply doesn't understand what it takes to operate a service business.
With the new "you're not my boss" mentality, (not to mention the side hustle program scammers) my guess is that we should expect to see a lot more of this moving forward.