How to remove specific numbers from a txt file with SED or AWK

awk '
    $1 == "Group" {printf("\\section{%s%d}\n", $1, $2); next}
    {for (i=1; i<=NF; i++) 
        if ($i ~ /^[0-9][0-9][0-9]$/) {
            printf("\\Testdetails{%d}\n", $i)
            break
        }
    }
' 

Update based on comment:

awk '
    $1 == "Group" {printf("\\section{%s %d}\n", $1, $2); next}
    {
      title = sep = ""
      for (i=1; i<=NF; i++) 
        if ($i ~ /^[0-9][0-9][0-9]$/) {
          printf("\\subsection{%s} \\Testdetails{%d}\n", title, $i)
          break
        }
        else {
          title = title sep $i
          sep = FS
        }
    }
' 

Since your file appears to consist of a sequence of records separated by one or more blank lines, I'd suggest trying something based on the paragraph modes of either awk or perl.

For example, if you always need to strip off the first two lines, like

1
00:00:00.096 --> 00:00:05.047

you could split into newline-delimited fields within blank-separated paragraphs and skip the first two fields using either

awk -vRS= -vORS= -F'\n' '{for(j=3;j<=NF;j++) print $j; print " "}' file.vtt

or

perl -F'\n' -00ne 'print join("", @F[2..$#F]), " "' file.vtt

If you can't rely on there being a fixed number of fields (lines) to be removed, then it's fairly easy to add a regular expression test - a little easier in perl since it allows us to grep directly on arrays rather than writing an explicit loop. For example, to split into blank-separated records and then print only those fields (lines) having at least one sequence of at least 3 alphabetic characters, you could use

perl -F'\n' -00ane '
  print join("", grep { /[[:alpha:]]{3}/ } @F), " "
' file.vtt

If you want to exclude the WEBVTT string you can simply skip the first record, i.e.

perl -F'\n' -00ane '
  print join("", grep { /[[:alpha:]]{3}/ } @F), " " if $. > 1
  ' file.vtt

It will be down to you to choose a suitable regex that capture the wanted lines and excludes the unwanted ones. You can add an END block in either awk or perl if you want to add a final newline to the concatenated output.

NOTE: since (based on the discussion in comments) your files appear to have DOS-style CRLF line endings, you will need to deal with those - either by modifying the field and record separators in the above commands accordingly, or by stripping out the CRs first e.g.

sed 's/\r$//' file.vtt | 
  perl -F'\n' -00ane '
    print join("", grep { /[[:alpha:]]{3}/ } @F), " " if $. > 1
  '
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