The plant your neighbor warned about is Pokeweed (Phytolacca americana). While mature plants are mildly toxic (mainly the deep taproot), the risk to a puppy is lower than many common household items.
Supervision and training are more effective than removing every mildly toxic plant.
— Advice from Susan
Toxic and Non-Toxic Houseplants for Cats
Hindu Rope Plant (Hoya) Safety for Dogs
Pokeweed (Phytolacca americana): Not Poison Ivy, But a Taprooted Volunteer
Elephant Foot Plant (Beaucarnea recurvata): Care for a Rescued Ponytail Palm
Bonsai Basics: Miniature Trees and Super Thrive
Bonsai Gift Plant: Ficus microcarpa
Mystery Plant from School Fundraiser Seeds: Deer Love It, But Is It Safe?
Euonymus Fortunei Leaf Drop and Brown Edges: Underwatering or Scale?
Lemon Plant Losing Leaves, Stem Drying: Critical Light Deficiency
Invasive Mint Control: No Allelopathic Plant Exists
Ornamental Cactus Crown Rot: Surgical Removal and Cultural Correction
White Substance on Gardenia: Mealybugs and Cold Hardiness
Identifying and Controlling Poison Ivy Safely and Effectively
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