The thing with mobile watchdog is it is not an app or software on the device. It is a service. You create an account to use the service, then you register devices to the service. To do that, you must know the AppleID and password each device uses with iCloud, as the service scans the iCloud backup for activity. You must also disable two factor authentication in each AppleID used with the service.
From the My Mobile Watchdog faq:
To configure an Apple product you will need the following information.
1. Your child's mobile number
2. Your child's iCloud ID and password
3. Your child's device must be connected to iCloud with Back Ups turned on and current. On your child's device you can see this under Settings>iCloud>Back Up
4. Two-factor authentication must be turned off on the child's iCloud ID
**There is not an app to install for iPhone**
So if you don’t share your AppleID and password with anyone, and you use two factor authentication, nobody can register your device with the service without your consent and knowledge.
My mobile watchdog seems to me to be a highly regarded and well reviewed parental minitoring software for iOS and Android. It is not malware and it does not allow use of the service anonymously or without peoples consent or knowledge. It even sends daily notifications about itself to all montored devices - again, form their FAQ
Yes, your child will know they are being monitored.
For children with Android phones, you will need to install an app on the phone. There is a visible My Mobile Watchdog icon on your child’s phone and we display a message daily.
So this is not malware, or a hack or anything malicious. Nothing is actually installed on an iOS device. Protect your AppleID and password and nobody can sign you up for the monitoring service surreptitiously.
One can only assume that the OP neither used two factor authentication, and has allowed their AppleID password to be known to others, and so someone signed up their device(s) with the service.