The earlier offer will be considered at a stockholders meeting on Sept.
In each case, the cash total is $2 more than the earlier offer.
The new bid values Lin at just under $6 billion, about $500 million lower than the earlier offer.
The plaintiffs would not be obliged to accept an early offer.
The earlier offer to the employee group expired on June 30.
In recent days, moreover, one country after another has improved its earlier offers.
The bank now says it will abide by the earlier offer.
"But I'll take you up on your earlier offer of another drink."
The earlier offer was $125 a share for 22 million shares.
Delta's management team, however, apparently decided it was willing to make some changes to its earlier offer.