As shown below we have a Calibration with a note that is not needed any more.  As shown below there is no option to delete the note.  These are the steps to do so.

WARNING - There is No way to Retrieve or Undo a Deleted Note!

There are two things that control whether a User can Delete Notes:

1.    The Company in which you want to Delete Notes must have the option to Delete Notes set.

2.    Your User must be in a 'User Group' that has "Delete" rights for the Record type in which you want to Delete the Note

Below is a screen shot of the Company record, Notes tab. The 'Delete Notes' option is not available because this User has only 'Modify' rights for the Company record.

This same User does have 'Delete' rights for Instruments, and the screen shot below does show the option to 'Delete Notes'.

Selecting the Delete Notes button will open a new screen:

Select the Row(s) that you wish to Delete and select the "Delete Selected Row(s)" button. You will receive the following Warning.

You will receive a Success message.

Clicking OK will return the Users to the "Delete Notes" screen without the Note(s) that were Deleted.

The below screen shows the Instrument record with only one of the two original Notes.

If you have Audit Trails turned on, there will be an Audit of the Deleted Note along with as much of the Note that will fit.