Airtable does not give us a way to split apart data from a field within a formula, so you will not be able to do this as an automatic feature within your table. However, it should be possible to make this happen using a script (or a script action within an automation).
The basic algorithm will be to split the contents of the tich text field on the line break character, check each row for a filled checkbox character and then re-join only the rows that do not have the filled checkbox character. You could maintain a second field (perhaps called “filtered summary”) where the script/automation outputs the filtered rich text.
EDIT: years later and I still forget about those regex functions! @Adam_TheTimeSavingCo’s solution is super clever!
Hmm, you could potentially try to do this via regex maybe, resulting in the following:

And from there you could manipulate it further for your email?
Link to base
And here’s the formula:
SUBSTITUTE(
REGEX_REPLACE(
Notes,
".+(+x].+)",
''
),
'\n\n',
'\n'
)
Hmm, you could potentially try to do this via regex maybe, resulting in the following:

And from there you could manipulate it further for your email?
Link to base
And here’s the formula:
SUBSTITUTE(
REGEX_REPLACE(
Notes,
".+(+x].+)",
''
),
'\n\n',
'\n'
)
Perfect! This is exactly what I needed. Thank you Adam!