In addition to an appeal to ratify the contract offer, which the union has urged workers to reject, the managers offered information about a decertification petition that may lead to a vote to remove the USW from representing the workers, said Bryan Gross, a representative of the international union.
"The company locked us out six months ago," Gross said. "They haven't asked about anybody and now they are reaching out and saying, 'Trust us.'"
An Exxon spokesperson did not immediately reply to a request for comment.
The 650 workers locked out on May 1 at the 369,024 barrel-per-day (bpd) refinery and lubricant-oil plant are scheduled to vote on Tuesday on Exxon's contract offer.
The company said in a message posted on Facebook on Friday that once the offer is ratified "the company will work with the union to establish a return to work agreement and return USW-represented employees to the site, ending the lockout."
The U.S. National Labor Relations Board is reviewing a petition submitted by at least 30% of the locked-out workers calling for a decertification vote. If successful, it would remove USW local union 13-243 in Beaumont from representing the workers.
The USW opposes opposing Exxon's contract offer, saying it would eliminate job seniority, which gives workers a say in job assignments, and create virtually separate agreements for refinery workers and lubricant plant workers.
Exxon has said the agreement is necessary to make the refinery competitive in even low-margin environments.
(Reporting by Erwin Seba; Editing by William Mallard)