You can't edit individual pixels... but you can look to see if I missed
Complete list of ArcGIS Image Analyst extension functions and tools—ArcGIS Pro | ArcGIS Desktop
In any event, it must be an aesthetic issue. If so, you can clip a small border area off, If it is for analysis, use a larger image area (if you have a sample of an existing one), then clip to size
I recommend you look to use ArcGIS Pro and the Image Classification Wizard. See The Image Classification Wizard—ArcGIS Pro | ArcGIS Desktop
This includes a reclassifier specifically designed to enable you to quickly make such edits. It leads you through the classification process including accuracy assessment and has nice tools to quickly select areas and change the classification.
Peter would that be accomplished by specifying the minimum segment size? or some other parameter (since there is no individual pixel editing that I can see)
Maximum Likelihood can be applied to pixel or segments. Yes, it appears that this UI only enables editing of the segment classification. Not sure why though. The process could just was well work with pixels. I'll try and find out why. What it does is set up a raster function chain that defines all the changes to be made and then saves a new image to persist the changes. In theory you can create a layer that defines such changes virtually and then either use this layer or save it as new/replacement raster.
You can change the value of individual pixels by code using numpy (which is installed with ArcGIS for Desktop). See the following example:
It's an old thread but I thought if you stumble upon it, you might find the following information useful:
Pixel Editor contains a set of tools used to interactively manipulate pixel values for raster and imagery data. It allows you to edit an individual pixel or a group of pixels at one time.
The Pixel Editor tools enable you to perform many editing tasks on your raster datasets:
Note: Pixel Editor is only available at ArcGIS Pro 2.4 onwards (not in ArcMap). Also it requires the Image Analyst extension.