Dynamic array resizing and nesting conditions
Looping through the Array, counting the matches to avoid resizing the return Array is very efficient.  

Application.Transpose is not needed because the return array is in the same shape as the original array.


  RemoveRows2D = Application.Transpose(arr_new)


This is correct:


  RemoveRows2D = arr_new


Using Application.Index to slice off the target column is a cool trick but is it really needed?  Not only does it add extra overhead but it adds an extra variable.  In my opinion, arr_col_k is just extra clutter because I don't think that  arr_col_k(i, 1) = strKeeper is any more readable than arr(i, x) = strKeeper.


  arr_col_k = Application.Index(arr, 0, k)


You can remove up_new = up_new + 1 from this loop:

If Headers Then                                   'handle header row
    For j = LBound(arr, 2) To UBound(arr, 2)
        arr_new(i, j) = arr(i, j)
    Next
    i = 1 + 1
    up_new = up_new + 1
End If


Moving forward, the main thing that I think you should focus on is the names of your variables.  Consider arr, k, strKeeper, up_new, arr_col_k, arr_new, what do the names of these variable tell you about the roles that they play?  

Compare them to my alternative names. 


arr: Data, DataArray, arrData, arrSource, Source, SourceArray
k: col, ColumnIndex
strKeeper:  Match 


I use Match because it is used in many VBA and Excel functions. 

up_new: Count
arr_col_k: Matches, arrTarget, ???I would have to think about this one. 
arr_new:  Results, results, arrResults


I also use 1 or 2 character variable names for all my counters.  I prefer x, x1, y, y1 because  i or l can be tough to differentiate. 

RemoveRows2D is basically a 2D version of the built in VBA.Filter function.  Whenever I write a version of a standardized method I start by copying the methods signature from the Object Browser and work from there.  Using the same structure and variable names as the built-in methods will make it easier for others to understand and use yours.

Question: Is there a more efficient way to nest the following:

If (arr_col_k(i, 1) = strKeeper And re_Tain) Or (arr_col_k(i, 1) &lt;&gt; strKeeper And Not re_Tain) Then


Technically, using If and EsleIf blocks is more efficient because the VBA evaluates all the conditions in an If Then statement.  In your case the difference in efficiency is negligible.  Note: In my version of function I use a flag with If and EsleIf blocks because I think that it read better and is easier to debug.

If (arr_col_k(i, 1) = strKeeper And re_Tain) Then

ElseIf (arr_col_k(i, 1) &lt;&gt; strKeeper And Not re_Tain) Then

End If




Function Filter2D(SourceArray, Match As String, ColumnIndex As Long, Headers As Boolean, Optional Include As Boolean = True, Optional Compare As VbCompareMethod = vbBinaryCompare) As Variant()
    Dim count As Long, x As Long, y As Long
    Dim flag As Boolean
    Dim Results() As Variant
    'Adjust the ColumnIndex based on SourceArray Lbound
    'This allows the user to refer to the 1st column of a Option Base 0 array as 1 instead of 0
    ColumnIndex = ColumnIndex - LBound(SourceArray, 2) + 1
    'First loop to count matches
    For x = LBound(SourceArray) To UBound(SourceArray)
        If x = LBound(SourceArray) And Headers Then
            count = count + 1
        ElseIf Include Then
            If StrComp(SourceArray(x, ColumnIndex), Match, Compare) = 0 Then count = count + 1
        Else
            If StrComp(SourceArray(x, ColumnIndex), Match, Compare) &lt;&gt; 0 Then count = count + 1
        End If
    Next

    If count = 0 Then Exit Function

    'Adjust the count based on SourceArray Lbound
    count = count - LBound(SourceArray) + 1
    'Size the Results array to fit the data
    ReDim Results(LBound(SourceArray) To count, LBound(SourceArray, 2) To UBound(SourceArray, 2))
    'Reset count for reuse
    count = LBound(SourceArray)
    'Second loop to transfer the data
    For x = LBound(SourceArray) To UBound(SourceArray)
        If x = LBound(SourceArray) And Headers Then
            flag = True
        ElseIf Include Then
            If StrComp(SourceArray(x, ColumnIndex), Match, Compare) = 0 Then flag = True
        Else
            If StrComp(SourceArray(x, ColumnIndex), Match, Compare) &lt;&gt; 0 Then flag = True
        End If

        If flag Then
            For y = LBound(SourceArray, 2) To UBound(SourceArray, 2)
                Results(count, y) = SourceArray(x, y)
            Next
            count = count + 1
        End If
        flag = False
    Next

    Filter2D = Results
End Function