Welcome, blueberry!
Appeals processes depend on the local educational authority in your area, as each one has different policies for identifying eligible students. Without knowing your specific LEA, only fairly general thoughts can be offered. (And please don't feel pressure to post any personal information you don't feel comfortable posting.)
But some general thoughts:
LEAs often use criteria such as cognitive screeners/measures (e.g., CogAT), achievement measures (e.g., iReady), grades (probably irrelevant at this grade level) and teacher nominations (often heavily weighted). In your DC's case, the cognitive measures are well above typical GT levels, but the achievement measures will depend on where they have decided to set the cutoff this year--which may not be a fixed number, as sometimes this has to do with the number of children/number of slots in program.
On the CogAT, 132 is +2 SD (98th %ile). It may be that the LEA has decided that students need to meet/exceed the 98th %ile on all measures to qualify, in which case the reading score would be the one measure that does not. Districts make different decisions on these cut scores. They are allowed to do so, as long as the criteria are applied equitably.
You certainly would be within your rights to inquire about the appeal process, and to request additional transparency regarding the selection process. If they use a holistic process (such as one including teacher comments or nominations), this might be met with less openness, mainly to protect the teacher from parent reprisals (which do happen, unfortunately).
