Hi John,
If my tenant wants something improved after moving in, it is at their expense only. As Sue Kelly stated earlier, they were happy with it at move-in. They might argue that you end up with a better property, which may be true, but you are happy with it as it is, or would have addressed it before leasing it out.
In all likelihood, your tenant will want to DIY it as much as possible to contain his costs (and hinted at with them wanting to rent the tiller). This raises the issue of a job going sideways and you ending up with a yard in worse shape than now, so you will want to protect yourself against that.
At the same time, from the tenant's perspective, if the job goes well, the property is in better shape then before and he might want protection against a rent increase in the near future because of that.
Both of these can be addressed with a written agreement and a remediation deposit refundable on satisfactory completion. You can figure out how much deposit to request based on getting the yard back to at least it's present state. At the same time, you can assure the tenant with appropriate wording in your agreement that the rent will not be increased other than by market conditions during the remainder of his tenancy. You should probably also state in the agreement that any plant/shrubs/trees put in place by the tenant during this overhaul become the property of, well, the property, again, as noted by Sue Kelly.
Looking at the pictures, I'd say the the yard would benefit substantially with just a mowing.
Good luck with your decision.
