While such examples are generally "obvious" to more experienced players (not that I don't see it happening even at single digit kyu level), I think it would be appropriate to include as an example a case where a player forces his opponent to expand his territory by stealing an eye. This sometimes applies to over-aggressive chasing of groups. The simplest example of this eye-stealing mistake is below.
This particular example is perhaps too simple. There are better examples where "expand his territory" is worth more than a point. In this case, the flaw in making use of such a thank you move is more severe. It is worth discussing this in the context of Miai. In cases where both are sente, the ideal would be to block off territory expansion rather than filling in eyes. But in the case where blocking off territory expansion is not sente but filling in the eyes is, it is often the case that neither move is good. The example above does not illustrate this point (blocking off territory is sente) and thus makes for a boring example.
I admit this type of Thank You Move is a bit elemenatary, but this particular page is on the introductary path.