In a general sense, Netrunner has fallen into what I like to think of as the "2, 3, 4" value principle. While 1 is almost always worth more than 1, in isolation the structure of 1:1:1Draw is typically a good place to start. Continuing this isolationist approach, every card played immediately costs a value of 2 (1 and 1Draw). Therefore cards that net you a positive value of 2 units are in essence, worthless since you could have obtained the value of 2 without the card by simply spending those s do gain resources naturally (looking at you Infiltration). A value of 3 is where things start to become positive, but are usually of too little impact still to justify use (I usually think of Easy Mark). A value of 4 or higher is really where cards start to shine, and at this point become near auto-includes to any deck that supports the card itself (the conventional Sure Gamble).
Within this backdrop, we can look at Greasing the Palm. Ignoring the required 3 upfront cost and its conditional tag-removing effect, this card gains you a value of 3 at 2 and 1 (from the install). This puts the card in the previously mentioned realm of "technically positive" but with there still probably being a better card to slot in somewhere. This means that in order to justify putting this card in your deck, you really need to be playing toward the tag-removal effect.
Removing said tag gives you a +2 value due to the free advancement token, which otherwise would have cost you a and a . If you can do this, suddenly Greasing the Palm is swinging at a total 5 value, greater than even Sure Gamble. Add to that, that this effectively fast-advances that card by 1 and you can see the clear advantage of Greasing the Palm.
Before we get too excited however, we must remember that the Runner must have a tag in the first place, and we remove it. Manual Runner removal of a tag is a 3 value tempo hit (2 and 1) and we are handing that over to them for free. It also means that we needed to invest resources into giving them the tag in the first place, which has also costs us a variable amount of value elsewhere. Lastly, the conditionality of the tag's existence, the Runner's ability to choose to remove that tag and the lack of ability to repeat the effect should we remove the final tag, makes this effect conditional and somewhat difficult to pull off reliably. So how do we slot this Event?
For starters, it needs to be in a deck that can give tags. Secondarily, if it is a deck that gives a small number of tags, then this probably needs to be the only tag-reliant effect that there is (since you will be removing said tag). Otherwise, it needs to be in a deck that gives the Runner so many tags that removing 1 is irrelevant. Lastly, it is worth mentioning that if you're playing against a Runner that just refuses to let those tags stick, you can still at least use it at a fairly reliable (if a bit weak) 3 value effect.
While the recent The Automata Initiative card release seems to be trying to spread some of the tag-love around to Corps other than just NBN, it would seem somewhat difficult for HB to innately make use of this. The effect is undeniably strong but my fear is that it will either never see use in-faction, or will simply be imported to NBN for some soul-crushingly efficient 3/2 scores. The issue I see with that however is that NBN already has plenty of fast advance in-faction (tag-reliant and otherwise) so splurging for this at a 3-influence cost even then may not be worth it.