I don't consider it screwing over the PC. I consider it making sure that it's a challenge for the player.
As someone whose 85lb mother owned a 170 lb very loyal and quite large dog, I don't think you need more challenge than 'it's very loyal. It also has its own logic about how the world works". For the beast, helping its master is showing loyalty and expecting reward - such as fetching. Now for a fledgeling griffon (or dragon), "fetching" is a bit different from what a human would think of. Next time it comes back with half a sheep, followed by a mob of angry villagers brandishing pitchforks and torches, the PC might realise there are caveats in the contract.
You can imagine hilarious situations that will result in increasingly severe problems for the PC until they realise that a griffon can be an asset when properly trained, housed, fed, and entertained, but is a huge liability on the road except in complete wilderness (and even then, the griffon can still stir up trouble with any monster in the area). Dragons are even worse because they have instinctive obsessions that can be very difficult to accommodate (such as the urge to accumulate treasure in a secure hoard).
Even an intelligent *cat* can be a full load of trouble. And it does not have to be a 30-year chore before the PC can reap benefits. Give them some of the expected benefits at once, and make that an interesting time - interesting enough that the PC is torn between wanting to keep the creature at all costs (because it is adorable, and very loyal, and pretty effective in certain situations) and ready to dump it at the earliest opportunity (because it acts on its instincts, frightens almost everyone who does not know it, ignores the societal order and its laws and rules, and stirs the nearest hornet's nest just because there was something juicy or shiny nearby).
Balance benefits and drawbacks. As the creature gets more powerful, the drawbacks will change or increase naturally, unless the PC really addresses the issue, making for a very different dynamics and either changing the relation (the creature becomes a very loyal occasional ally) or changing the PC lifestyle completely. And the player will be the one to decide how they solve the problem (with a little push from their friends).
But warn the player beforehand. It's not a free ride: you will have to deal with the consequences, including the negative ones.
