No it's not possible... [YES it's possible as the code below shows]
The discrete Fourier transform of an image is a decomposition of it into an orthogonal set of periodic sine (complex exponential) waves. Intensity domain information is best dealt with spatial domain processing, which can be nonlinear type of operations without a (useful or simple) frequency domain counterpart, except some trivial cases (as below).
EDIT: [I'm sorry but I was wrong]
Now after Royi's comment, I realised the fact that I was plain wrong in what I meant. The correct answer is that yes of course you can remove the bright pixels (or any selected set of pixels, as given by a spatial mask) in an image through frequency domain manipulation. The only thing to note is that, however, that's plain inefficient when compared to the equivalent spatial-domain processing...
Indeed the following MATLAB/OCTAVE excerpt just shows it:
x = double(imread('Cameraman.tif')); % image range in [0:255]
S = size(x);
N = S(1);
M = S(2);
h = double( x > 200); % select a set of pixels into mask
y = x.*h; % apply spatial-domain masking
% perform the masking in freq domain:
X = fft2(x);
H = fft2(h);
ylin = conv2(X,H); % get the linear convolution
yc = zeros(N,M); % yc is the periodic conv
yc = ylin(1:N,1:M) + [ ylin(N+1:end,1:M); zeros(1,M)] + ...
[ylin(1:N,M+1:end) ,zeros(N,1)] + [ylin(N+1:end,M+1:end),zeros(N-1,1); zeros(1,M)];
Yc = real(ifft2(yc)/(N*M));
figure,imshow(x/255); % original image
figure,imshow(y/255); % masked in spatial-domain
figure,imshow(Yc/255); % masked in frequency domain
figure,stem3(y-Yc); % the difference sequence