They are not entitled to do so -- public schools do not have authority over private schools.  It would be like the public school principal going to the parochial school and demanding to see (or inspect) their curriculum and attendance. 

To combat this problem state-wide, Tim Lambert of the Texas Home School Coalition approached Dr. Mike Moses, then Commissioner of Education, to clarify the TEA position Dr. Moses wrote a letter to all districts giving direction on how to deal with families who seek to teach their children at home.

Commission Nelson (current) has sent out an updated letter, available http://www.thsc.org/about_us/commissioners_letter.asp

Side note:  Through experience we know that the vast majority of homeschoolers never face any problems with the school district, they have enough work dealing with the students who are enrolled.  Most just want to finish their paper work so they know not to report the student absent.

Taking them out of public school and starting homeschooling is often as simple as going to the public school and telling them your intent to put them in a private school and returning any books you may have. 

Knowing that the court decision rendered in Leeper vs. Arlington clearly establishes that students who are home schooled are exempt from the compulsory attendance requirement to the same extent as students enrolled in private schools, may be of help your confidence if you are faced with a problem administrator. 

Your home private school curriculum should be designed to meet basic education goals including reading, spelling, grammar, mathematics, and study of good citizenship.  This can easily be done using the library and the internet, and doesn't require you to purchase any preset curriculum.