I would argue based on context, that this is a Hebraic way of saying, 'partaking' in Christ (knowledge is intimately related to intimacy, of which the euphemism, 'to know,' meaning, 'to engage in the sexual act with' is a key, and telling example).
See how he introduces his letter:
Simon Peter, servant and apostle of Jesus Christ, to them that have obtained equal faith with us in the righteousness of our God and Saviour Jesus Christ. 2 Grace to you and peace be multiplied in the knowledge of God and of Christ Jesus our Lord: 3 As all things of his divine power which appertain to life and godliness, are given us, through the knowledge of him who hath called us by his own proper glory and virtue. 4 By whom he hath given us most great and precious promises: that by these you may be made partakers of the divine nature: flying the corruption of that concupiscence which is in the world.
The knowledge of Jesus seems to mean, 'having come to know him through a justifying personal relationship.' How else could one have grace or become a partaker of the divine nature, or escape the corruption of concupiscence, death, and the world? Such things could and would never be said of someone steeped in sin.
Notice that he says, for example, that people "escape" this world and its evils via this "knowledge," and that he uses the proverb about 'being washed' and returning to the mire - what can only be taken to refer to having been cleansed from sin, and then returned to it - a dog returning to what it vomitted up and got rid of:
2 Peter 2:20-22 Peter For if, flying from the pollutions of the world, through the knowledge of our Lord and Saviour Jesus Christ, they be again entangled in them and overcome: their latter state is become unto them worse than the former. 21 For it had been better for them not to have known the way of justice, than after they have known it, to turn back from that holy commandment which was delivered to them. 22 For, that of the true proverb has happened to them: The dog is returned to his vomit: and, The sow that was washed, to her wallowing in the mire.
Notice also the word "again," as in they escaped and were removed from such by a saving knowledge of Christ, for which reason it is "better" they had never known the way of truth to begin with. Otherwise the word "again" could not be used, since it denotes a distinction between what was, what ceased for a time, and then began again: whereas here it refers to sinning wilfully or as a way of life.
This comports with the teaching of Hebrews:
Hebrews 10:26-30 For if we sin wilfully after having the knowledge of the truth, there is now left no sacrifice for sins, 27 But a certain dreadful expectation of judgment, and the rage of a fire which shall consume the adversaries. 28 A man making void the law of Moses, dieth without any mercy under two or three witnesses: 29 How much more, do you think he deserveth worse punishments, who hath trodden under foot the Son of God, and hath esteemed the blood of the testament unclean, by which he was sanctified, and hath offered an affront to the Spirit of grace? 30 For we know him that hath said: Vengeance belongeth to me, and I will repay. And again: The Lord shall judge his people.
What is a worse punishment than dying without mercy? Only eternal death. After all, this man was "sanctified" by the blood of Jesus, and is "[one of God's] people," which is why this kind of sinner (apostate) is such an affront to the Spirit of grace.
Thus it seems to denote more than just being aware of the teaching of Christ, but having lived in it but for a time.
Luke 8:13 Now they upon the rock, are they who when they hear, receive the word with joy: and these have no roots; for they believe for a while, and in time of temptation, they fall away.