No, do not do this. I will preface my comment to you by stating that I am an engineer and have have been a contractor in heavy civil construction for 25+ years building roads, bridges and complex civil works. I have years of experience with mechanically stabilized earth walls which includes geo grid walls. We use geo grid walls as temporary walls with a wire face for phased construction.
The geo grid tie back is absolutely necessary even though it may seem like to the layman that it is not. You would be surprised how much force that geo grid will resist as it may not seem strong but when wedges between dirt layers it resists a lot of force.
1) Using filter fabric can reduce the drainage behind the wall which will creat unnecessary head pressure against the wall and can cause it to blow out, unless it was specifically designed that way. The geo grid is free draining and does not have this issue.
2) The fact that you have a solid wall is only that, the wall is solid. It could be a foot think steel plate standing up but unless there is something keeping it from tipping over(tiebacks like the geogrid or chance anchors) the stiffness of the wall means nothing when it is being used to retain earth because their is nothing to resist the moment(overturning force) the wall is feeling.
Install the geogrid per the manufactures specifications for a wall that height. Use the proper backfill. Clay and silty material does not work as it has slip planes in the material(hence why clay is so slippery when wet). It need to be free draining sandy material without organics.
Do not compact to hard next to the wall as you it is not the hard to move the wall out of place. Consider some minimal hydro compaction within 3 foot of the wall after a very lightly compacting mechanically. Out side of three feet you should be good but start at the middle of the geogrid and compact away from the wall and then come back and compact towards the wall.
Im sure there is lots of videos and literature online to watch but you you absolutely have to properly tie back that wall or it will fail.