Of course – though the dog may sulk! In Settings, open Display Settings, find Pets and untick "Show pets on the tree". The pets aren't deleted: their pages, pictures and owners are all kept, and ticking the box again brings them straight back. If you can't see this setting, ask your tree owner or admins.
Where to find it
Settings (bottom row of the top bar, far right) → Display Settings
On a phone: if the Settings tabs are tucked away, press ☰ Menu (top left) first.
Still stuck? Talk to a real person: send us a message, or email support@mywholefamilytree.com