Michelle Marie Thompson, of Arvada, Colo., was first noticed walking around the facility early on the morning of February 26, a Mets staffer said.
Thompson reportedly loitered for hours, telling officials that she and Tebow were in a relationship.
The officer asked if the relationship was friendly, platonic, romantic or matrimonial, Thompson giggled and said "all of the above".
Thompson told officers that the Colorado address on her license was not current because she was living with Tim Tebow in Jacksonville.
Thompson was given a trespass warning, and she left the property.
After the woman turned over her driver's license, the officer noticed a small sticker with the words "I (heart) Jesus/Tim Tebow".
"I thought you walk around because you're a left-hander", he said after the New York Mets' 8-7 win over the Boston Red Sox.
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According to online records, Thompson was still in the St. Lucie County Jail on $750 bond as of Friday afternoon.
The trespass warning was explained to Thompson "two times to ensure clarity", according to the documents.
Tebow briefly questioned the home plate umpire on each of his strikeouts, saying later that he questioned whether the pitches weren't outside the strike zone.
Mets executive director of minor league facilities Paul Taglieri told police the woman had been walking around the complex since the early morning of the incident asking about Tebow.
This week, Tebow faced reigning AL Cy Young Award victor Rick Porcello during a Grapefruit League game, and struck out looking.
Tebow was set to lead off the third inning for his first at-bat. The former Heisman Trophy victor from the University of Florida also was picked off first base after being hit by a pitch in that game. He had two whiffs in the game and also grounded into a double play.