You could call Animal Poison Control (if you have an annual Home Again membership on his microchip, this should be a free call - otherwise $60). That is what I would do. (and have done when mine at Baklava, Rhododendrums ...etc.!).
We had a lot of poisonous plants in our yard when we moved in. We killed the Lilies of the Valley with Vinegar - they were popping up inside a brick patio, so that worked for us, no grass to kill. I guess you can't really control the landscaping since you are renting?
(a.k.a. Lucky's & Sparky's mom!)