The "Grainger" test is an interpretation of "philosophical belief" under the Employment Equality (Religion or Belief) Regulations 2003 (repealed, but the relevant portions of which are now included in the Equality Act 2010; it says, "Belief means any religious or philosophical belief").
I see three avenues for change: legislative reform; an appeal to the Court of Appeal; or convincing the Employment Appeal Tribunal that it is using the wrong test.
Legislative reform
Given that this is a statutory protection, if the legislative branch believes a tribunal or judiciary has misinterpreted it or believes that it is no longer appropriate, this protection for philosophical beliefs could be removed or clarified by an Act of Parliament.
Appeal
The Grainger test was developed by the Employment Appeal Tribunal and applied by Employment Tribunals since. There are procedures for judicial review of tribunal decisions. One could appeal an application of the Grainger test by the Employment Appeal Tribunal. It would end up at the Court of Appeal which could potentially announce that the Grainger test for what makes something a "philosophical belief" is the wrong test.
Convince the tribunal the Grainger test is the wrong test
The Employment Appeal Tribunal is free to update the approach to the term "philosophical belief." If the current approach is unworkable in some way, one might convince the tribunal it needs to update the test.1
This was a power grant not a power grab
I now am moving beyond the literal scope of your question to address what I see as unstated premises behind your question.
The Employment Appeal Tribunal is a tribunal, not a court. While it is a part of a unified judicial system, and its members are guaranteed judicial independence, it is part of the administrative state. Parliament expressly granted jurisdiction to the Employment Appeal Tribunal to hear appeals "arising in any proceedings before an employment tribunal under or by virtue of ... the Equality Act 2010" (see Employment Tribunals Act 1996, s. 21, as amended). Parliament chose this expert, specialized tribunal to have the jurisdiction to decide how to interpret and apply the Equality Act 2010. Courts are loathe to interfere with an interpretation or decision made by an administrative tribunal, as this would upset the choice made by Parliament to let the administrative body make the decision. They are, however, reviewable for errors of law (Anisminic Ltd. v. Foreign Compensation Commission, [1969] 2 AC 147). In the case of the Employment Appeals Tribunal, Parliament has even provided an express path for appeal to the Court of Appeal. This is an area of law where Parliament has dictated which administrative bod(ies) should make the initial determinations regarding the interpretation and application of the Equality Act 2010 and provided a precise mechanism for challenging those decisions.
I've focused on the administrative nature of Employment Tribunals and the Employment Appeal Tribunal, but if this question were to come directly before the judiciary, the issue would still be that Parliament has provided protection for "any religious or philosophical belief." When a claim of discrimination based on a philisophical belief comes before these tribunals or ultimately the Court of Appeal, they will have to somehow decide whether the complainant's belief is a philosophical belief warranting protection under the Equality Act 2010.
1. While stare decisis is a factor, tribunals are not bound by stare decisis towards their own previous decisions in the same way as courts tend to be. Also, most entities that respect stare decisis have a principled way of reconsidering their previous positions on questions of law (when not constrained by precedent from higher courts). That is, an institution's conception of stare decisis has built in a theory about when it is okay to depart.
