In this context, the phrase "there are no equitable considerations that would require the court to reduce or deny reimbursement for the parents" largely refers to defenses to claims arising under the law of equity as applied historically in the chancery courts of England, and more recently, to claims of a type that would have been brought in equity courts if there were still a separate equity court system.
Two of the more common equitable defenses are "unclean hands" and "laches".
The equitable defense of "unclean hands" applies when the person seeking relief has engaged in misconduct of some kind in the same transaction.
For example, if "the student was denied a FAPE at their public school placement" because the student had previously been expelled for beating up another kid (especially if this had nothing to do with the reason that a FAPE is needed) or because the parents ignored a deadline for filing the application for a FAPE at their public school of which they had reasonable advanced notice, that student's parents might be denied reimbursement under the doctrine of unclean hands.
The equitable defense of "laches" applies when unreasonable delay on the part of the person seeking relief causes prejudice to the person from whom relief is sought even in the absence of a date certain deadline or before a date certain deadline expires.
For example, suppose that "the private school was an appropriate placement" but it had tuition three times as high as two other private schools in town. If the other two less expensive private schools had vacancies for months after the student was denied a FAPE at their public school placement, but had no room for new students a week before school started leaving only the much more expensive private school with any vacancies, the request might be denied, or limited to the amount that would have been paid if the parents had applied to other private schools more promptly, under the doctrine of laches.
Other equitable defenses include the duty to mitigate damages (e.g. there might be reimbursement for private school tuition, but not for late fees and interest that could have been avoided), impossibility and impracticability (e.g. no public or private placement is capable of addressing the fundamental problem that the child is in a catatonic state), acts of god/force majeure (e.g. the student was denied a FAPE because the school was destroyed in a hurricane and the school district had to shut down the schools for everyone for a semester), implied waiver or estoppel (e.g. after the student was denied a FAPE the student was enrolled for regular classes at that public school without complaint and without trying to find a private school placement), spoliation (e.g. the records needed to determine eligibility were intentionally destroyed by the applicant before the hearing), fraud as a defense and not a claim (e.g. the parents lied in their reimbursement application), payment (e.g. the student was denied a FAPE by two schools and already received reimbursement from another one and is not entitled to a double recovery), release or accord and satisfaction (e.g. a settlement agreement was already reached with the school denying reimbursement or agreeing to a particular reimbursement).
