TypeScript: How to use generic types on abstract class as parameter type hints?

I have an abstract class:

abstract class Connector<T> {
  abstract parse(theirData: T[]): OurData[]
}

However, concrete subclasses do not infer the method types from the type parameter:

class APIConnector extends Connector<string> {
  // Parameter 'theirData' and return type implicitly has an 'any' type.
  parse(theirData) {
    ...
    return connection
  }
}

Maybe I am misunderstanding the purpose of TypeScript in this particular instance, but why would the inherited abstract methods not infer the type from the generics? It seems to defeat the point if I have to additionally type-hint the parameter and return types.

I understand that by using generics I am prevented from creating a bad signature for this method, but then if TS already knows what the type is then why would it state it as "implicit any"? Is this an option or something I can toggle in tsconfig?