I couldn't open your pdf (antivirus said it was suspicious) so i downloaded an image myself, I don't know if its the right one, but its also from a 1920 census
You could perform image dilation on the document until the text is gone. You can do multiple passes if needed. I just did one. We know dilation will make shrink the black sections (or the text) this essentially gives us just the background.
We then remove the background from the image. This can be tricky depending on the language (I used matlab, and had to make sure to keep the right range and units for the image to display properly) then you have a cleaner image. You should be able to run a ocr engine on the result
and here is a zoomed in section just so you can see the text quality doesn't degrade much with this operation
and of course the code. As I said it is done in matlab but openCv(in many languages), python, or just about any other image library will be able to perform a similar operation
im = rgb2gray(color_im);
bg = imdilate(im,strel('disk',3));
%we do a complement becasue the bg subtraction makes the text white and
%the background black. so we invert it
clean = imcomplement(abs(bg-im));
subplot(1,3,1); imshow(im); title('original')
subplot(1,3,2); imshow(bg); title('after imdilate with 3 pixel circle')
subplot(1,3,3); imshow(clean); title('original minus background')
and here is the image I used. Its the first page of the 1920 census https://archive.org/details/fourteenthcensus02unit
edit
I forgot you said it was handwritten images. so I got another sample, same exact code, new image
notice the detail even in very dark obscured places, as the zoomed in view shows. You would need to run some other filters, but removing the main background noise is accomplished using dilation
