INA 244(f) (4) said TPS grantees are: "Considered as being in and maintaining lawful status in the U.S. as non-immgrant for purposes of Adjustment of Status under section 245 of the Act and Change of Status under section 248 of the Act".
There is no mention in whatsoever about whether or not if the TPS recipient entered lawfully.
As fact, aliens with lawful entry can adust status to Lawful Permanent Resident with petition from U.S.citizen mates at any time; even after they overstay their visa (become illegal). Clearly there is no need for them to get TPS to adjust their status...
Then, what is the real deal about TPS & adjustment of status?