Designing High Pass Filter to Remove DC Offset from a Signal
If the DFT is the Uniform sampling from $ 0 $ to $ 2 \pi $ then the first bin is given by:

$$ x[k] = \sum_{n = 0}^{N - 1} x[n] $$

Namely it is the sum of all the samples.
Hence in order to remove the DC (Mean) all you need is a filter which has zero in its DC bin.
Since, the filtered signal, which is a convolution (Circular) of the DFT of the input signal and the filter will have zero at the first bin which means the sum of the output is zero which means its mean is also zero, as wanted.

Simple and intuitive FIT would be an FIR with the length of signal which removes from the current sample the mean of all samples:

$$ y[m] = x[m] - \frac{1}{N} \sum_{n = 0}^{N - 1} x[n] $$

This is a simple FIR.

Pay attention I assumed you have all the samples.
If you don't, you need to make this FIR casual by only "Calculating" the sum of given samples.