More stringent vetting of sports recruits. An external review of coach admissions recommendations. New policies on accepting team gifts.

After an embarrassing couple of weeks entrenched in a nationwide college admissions scandal, Stanford officials said this week that they are reworking how athletes are accepted by the school in an attempt to regain the trust of the public, alumni and student body.

“We know that this episode has jarred the trust of many Americans in the college admissions process, and it has prompted many questions from the Stanford community,” President Marc Tessier-Lavigne and Provost Persis Drell wrote in a blog post. “We are determined to take the right steps at Stanford to ensure the integrity of our process and to work toward rebuilding that trust.”

Last week, Stanford’s head sailing coach, John Vandemoer, pleaded guilty to accepting $770,000 in bribes to help recruit two students with minimal sailing experience onto his team. Neither student wound up attending Stanford, but a third did with bogus sailing credentials. Vandemoer was immediately fired and has accepted a plea deal that could send him to prison for 18 months.

In the update, school officials said they continue to “work to verify the circumstances around this student and will take whatever actions are appropriate.” They said the $500,000 contribution linked to the student was made several months after she was admitted.

The college is not aware of other students or donations to the school linked to the wider scandal, the officials said.

“Since the admission fraud came to light last week, we have been working to address the clear issues it has laid bare, as well as to look for additional issues that we need to attend to,” the president and provost said.

The school will launch an external review of the athletic department recommendation system. During Vandemoer’s court appearance, federal prosecutor Eric Rosen described a system in which recruits are first screened by admissions officers prior to submitting an application. If the student’s transcripts and test scores are reasonable, Rosen said, the office will let the coach mail a “pink envelope application” to the student.

“Being a recipient of a pink envelope application and being recruited is a significant material benefit to an applicant, as the acceptance rate for those granted the pink envelope status or recruited athlete status is much higher than those applicants who are not recruited athletes,” Rosen told the judge last week.

He said each coach gets a certain number of pink envelopes. Stanford has argued that no coach gets any guaranteed spots and each recruit still must meet academic standards.

Even so, the president and provost said, a higher-up in the athletics department will now “review and confirm” the athletic credentials for recruits in all 36 varsity men’s and women’s sports, providing an added layer of oversight.

The school has reviewed the athletic credentials for all its current sailors dating back to 2011 and found them to be legitimate.

The school will also review rules over teams accepting gifts. It also is working with the California attorney general’s office to determine how to redistribute the $770,000 the sailing team received as part of the scandal.

Stanford will admit a new class of undergrads this month, and the college has reviewed the athletic credentials of recruits and found no evidence of bogus resumes. No applicants are linked to any donations from the bogus charity linked to scandal either, the school officials said.

Matthias Gafni is a San Francisco Chronicle staff writer. Email: matthias.gafni@sfchronicle.com Twitter: @mgafni