Invite to what?

[Niwashi]

You can hit the monster on your own (solo) but if there is a party hunting it as well then you wont do enough overall damage and likely won't get credit for doing it.
Thus the reason for the invite.

More specifically, you're unlikely to get full credit solo. The minimum you can get is 4 Allied Seals and 3 Poetics tomes just for tagging an A rank as opposed to getting up to 40 seals and 30 tomes if you and your party do major damage to it. There are also some intermediate levels in between those for players who did more than just tag it but not quite enough for full credit. (For an S rank, full credit is 100 of each, so I expect the lowest tagging score would net around 10 each if they have the same 1/10 pattern as on A ranks.)