The items shown in the gamemode switcher are hardcoded and cannot be reconfigured in any way. This affects all four items in the gamemode switcher; creative (grass block), survival (iron sword), adventure (empty map), and spectator (eye of ender).

Suggested Fix:

There are two ways this can be fixed, outlined below:

1. Allow the items to be reconfigurable via data packs
   Similar to the advancement tabs, the player would be able to configure the items shown by choosing which item to display for each gamemode slot. As a comparison, this datapack changes the end stone of the The End tab to regular stone:
   
   
   While this comparison is not totally fair considering their functional difference, it still showcases a willingness currently to allow the player to alter vanilla items shown in screens/menus.
2. Allow the items to be changed via resource pack sprites
   Introduce sprite textures for each of the items, similar to the items/icons in the statistics screen:
   

Notes:

1. This issue very well may be a feature request, but was reported anyways because I was not sure if items or blocks in screens/menus being hardcoded/unconfigurable could be considered a bug.
2. May be related to these issues (I'm unsure considering their more texture focussed):
   MC-270260 MC-270254 MC-270255 MC-264571 MC-270766