Waitress Kelly Carter said a couple had written on the receipt: "Great service don't tip black people."
Owner Tommy Tellez told BBC News the response has been "phenomenal".
People have been dropping by the restaurant to give Ms Carter cash, Mr Tellez said, and a YouCaring campaign has raised over $300 (£245) for her.
Her regular customers have been dropping by to give her hugs.
Tipping is customary in the US, where restaurant servers often earn less than the minimum wage, with tips supposed to make up the difference in pay.
The white couple who left the note appeared to be in their mid-20s, and left after spending $30.52 (£25) on food.
Ms Carter told local media that one of the diners had even complimented the breakfast she served them on Saturday.
She says that she would gladly serve the pair again, adding "one hateful remark cannot stop me" and that she would recognise them if they returned to Anita's New Mexico Style Cafe.
"My arms are still opened to him," she said, offering to serve them again.
"That's him, not me," she said during her morning shift one day after the incident, adding that "he only hurt himself. He only makes me stronger."
Anita's owner Mr Tellez said that Ms Carter has "handled it very well" and that he agrees with her desire to serve the pair again.
"Two wrongs don't make a right", he told the BBC, adding that the note was "appalling, disheartening, and outrageous".
He thinks political rhetoric from the 2016 presidential campaign means that "racism has certainly been on the table the last 18 months" and has thrown fuel on "a fire that has never gone out" in the US.
Ms Carter says she really does hope to see the couple again.
"Just me serving them will let them know they did not get the best of me. And I truly mean that."